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Thierry E. Huillet

Thierry E. Huillet
Laboratory of Physics: Theory and Models (LPTM), CNRS UMR-8089

PhD

About

174
Publications
15,420
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767
Citations
Citations since 2017
42 Research Items
303 Citations
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20172018201920202021202220230102030405060
20172018201920202021202220230102030405060
20172018201920202021202220230102030405060
Additional affiliations
January 2001 - September 2022
Cergy-Paris University (CYU)
Position
  • CNRS Researcher
January 2000 - December 2014
Laboratory of Physics: Theory and Models (LPTM)
Position
  • CNRS Researcher

Publications

Publications (174)
Preprint
For super-heated water on a substrate with hydrophobic patches immersed in a hydrophilic matrix, one can choose the temperature so that micro-bubbles will form, grow and merge on the hydrophobic patches and not on the hydrophilic matrix. Until covering a patch, making a pinned macro-bubble, a bubble has a contact angle $\pi-\theta_2$, where $\theta...
Article
We consider continuous space–time decay–surge population models, which are semi-stochastic processes for which deterministically declining populations, bound to fade away, are reinvigorated at random times by bursts or surges of random sizes. In a particular separable framework (in a sense made precise below) we provide explicit formulae for the sc...
Article
Full-text available
In a family of random variables, Taylor's law or Taylor's power law of fluctuation scaling is a variance function that gives the variance $\sigma ^{2}>0$ of a random variable (rv) $X$ with expectation $\mu >0$ as a power of $\mu$: $\sigma ^{2}=A\mu ^{b}$ for finite real $A>0,\ b$ that are the same for all rvs in the family. Equivalently, TL holds w...
Preprint
In a family of random variables, Taylor's law or Taylor's power law offluctuation scaling is a variance function that gives the variance $\sigma^{2}>0$ of a random variable (rv) $X$ with expectation $\mu >0$ as a powerof $\mu$: $\sigma ^{2}=A\mu ^{b}$ for finite real $A>0,\ b$ that are thesame for all rvs in the family. Equivalently, TL holds when...
Article
The two-parameters generalized Sibuya discrete distributions capture the essence of random phenomena presenting large probability mass near the lower bound of its support balanced with heavy-tails in their deep upper bound. They are heavy-tailed as a result of the reinforcement mechanism that produced them, related to the modern notion of preferent...
Preprint
For super-heated water on a substrate with hydrophobic patches immersed in a hydrophilic matrix, one can choose the temperature so that micro-bubbles will form, grow and merge on the hydrophobic patches and not on the hydrophilic matrix. Until covering a patch, making a pinned macro-bubble, a bubble has a contact angle π − θ 2 , where θ 2 is the re...
Preprint
Full-text available
Inspired by the stenocara beetle, we study an ideal flat surface composed of a regular array of hydrophilic circular patches in a hydrophobic matrix on an incline of tilt $\alpha$ with respect to the horizontal. Based on an exact solution of the Laplace-Young equation at first order in the Bond number, the liquid storage capacity of the surface is...
Article
Water harvesting is a critical and very urgent problem for humanity. Inspired by the stenocara beetle, we demonstrate from first principles how heterogeneous wettability surfaces can optimize water collection by varying the area of hydrophilic patches on top of a hydrophobic surface. These theoretical considerations allow to determine the best comb...
Preprint
Full-text available
A Bernoulli scheme with unequal harmonic success probabilities is investigated, together with some of its natural extensions. The study includes the number of successes over some time window, the times to (between) successive successes and the time to the first success. Large sample asymp-totics, statistical parameter estimation, and relations to S...
Article
In this article, we study a particular class of Piecewise deterministic Markov processes (PDMP’s) which are semi-stochastic catastrophe versions of deterministic population growth models. In between successive jumps the process follows a flow describing deterministic population growth. Moreover, at random jump times, governed by state-dependent rat...
Preprint
Full-text available
We study a class of Cannings models with population size N having a mixed multinomial offspring distribution with random success probabilities W 1 ,. .. , W N induced by an independent and identically distributed sequence of positive random variables X 1 , X 2 ,. .. via W i := X i /S N , i ∈ {1,. .. , N }, where S N := X 1 + · · · + X N. The ancest...
Article
Recurrence and transience conditions are made explicit in discrete-time Markov chain population models for which random stationary growth alternates with disastrous random life-taking events. These events either have moderate stationary magnitudes or lead to an abrupt population decline. The probability of their occurrence may or may not depend on...
Article
Full-text available
Lamperti's maximal branching process is revisited, with emphasis on the description of the shape of the invariant measures in both the recurrent and transient regimes. A truncated version of this chain is exhibited, preserving the monotonicity of the original Lamperti chain supported by the integers. The Brown theory of hitting times applies to the...
Preprint
Full-text available
Shot-noise models deals with the cumulative output of a system whose input is subject to a random Poisson succession of equally distributed impulses or shots, each followed by some attenuation dynamics. With population dynamics in mind, we study the cases when the attenuation dynamics is either given by some ad hoc attenuation function or by some n...
Article
The analytical expressions of liquid-vapor equilibrium contact angles are analyzed in the thermodynamic limit for various simple geometries and arrangements of the substrate, in particular when the latter exhibits two or more scales. It concerns the Wenzel state of wetting when the substrate is completely wet, the Cassie-Baxter state when the liqui...
Article
In a Markov chain population model subject to catastrophes, random immigration events (birth), promoting growth, are in balance with the effect of binomial catastrophes that cause recurrent mass removal (death). Using a generating function approach, we study two versions of such population models when the binomial catastrophic events are of a sligh...
Preprint
Catastrophe Markov chain population models have received a lot of attention in the recent past. We herewith consider two special cases of such models involving total disasters, both in discrete and in continuous-time. Depending on the parameters range, the two models can show up a recurrence/transience transition and, in the critical case, a positi...
Preprint
In a Markov chain population model subject to catastrophes, random immigration events (birth), promoting growth, are in balance with the effect of binomial catastrophes that cause recurrent mass removal (death). Using a generating function approach, we study two versions of such population models when the binomial catastrophic events are of a sligh...
Article
For a pendent drop whose contact line is a circle of radius r0, we derive the Furmidge-like relation mgsinα=π2γr0(cosθmin−cosθmax) at first order in the Bond number, where θmin and θmax are the contact angles at the back (uphill) and at the front (downhill), m is the mass of the drop and γ the surface tension of the liquid. The Bond (or Eötvös) num...
Preprint
[To appear in Advances in Applied Probability 55.2] Continuous space-time decay surge population models are those semi-stochastic ones for which deterministically declining populations, bound to fade away, are reinvigorated at random times by bursts or surges of random sizes, resulting in a subtle asymptotic balance. Making use of the notion of sca...
Preprint
Full-text available
Continuous space-time decay surge population models are those semi-stochastic ones for which deterministically declining populations, bound to fade away, are reinvigorated at random times by bursts or surges of random sizes, resulting in a subtle asymptotic balance. Making use of the notion of scale functions, we exhibit conditions under which such...
Article
Full-text available
Exact mathematical identities are presented between the relevant parameters of droplets displaying circular contact boundary based on flat tilted surfaces. Two of the identities are derived from the force balance, and one from the torque balance. The tilt surfaces cover the full range of inclinations for sessile or pendant drops, including the inte...
Preprint
The analytical expressions of liquid-vapor macroscopic contact angles are analyzed for various simple geometries and arrangements of the substrate, in particular when the latter exhibits two or more scales. It concerns the Wenzel state of wetting when the substrate is completely wet, the Cassie-Baxter state when the liquid hangs over the substrate,...
Preprint
Deterministic population growth models can exhibit a large variety of flows, ranging from algebraic, exponential to hyper-exponential (with finite time explosion). They describe the growth for the size (or mass) of some population as time goes by. Variants of such models are introduced allowing logarithmic, exp-algebraic or even doubly exponential...
Article
Some population is made of n individuals that can be of P possible species (or types) at equilibrium. How are individuals scattered among types? We study two random scenarios of such species abundance distributions. In the first one, each species grows from independent founders according to a Galton-Watson branching process. When the number of foun...
Article
Full-text available
Catastrophe Markov chain population models have received a lot of attention in the recent past. We herewith consider two special cases of such models involving total disasters, both in discrete and in continuous-time. Depending on the parameters range, the two models can show up a recur-rence/transience transition and, in the critical case, a posit...
Preprint
Catastrophe Markov chain population models have received a lot of attention in the recent past. Besides systematic random immigration events promoting growth, we study a particular case of populations simultaneously subject to the effect of geometric catastrophes that cause recurrent mass removal. We describe the subtle balance between the two such...
Preprint
Lamperti's maximal branching process is revisited, with emphasis on the description of the shape of the invariant measures in both the recurrent and transient regimes. A truncated version of this chain is exhibited, preserving the monotonicity of the original Lamperti chain supported by the integers. The Brown theory of hitting times applies to the...
Article
Full-text available
Two problems dealing with the random skewed splitting of some population into J different types are considered. In a first discrete setup, the sizes of the sub-populations come from independent shifted-geometric with unequal characteristics. Various J → ∞ asymptotics of the induced occupancies are investigated: the total population size, the number...
Preprint
Full-text available
We study properties of truncations in the dual and intertwining process in the monotone case. The main properties are stated for the time-reversed process and the time of absorption of the truncated intertwining process. Published in Markov Processes and Related Fields. 26, Issue 3, 423-445, 2020.
Article
The Sibuya distribution is a discrete probability distribution on the positive integers which, while Poisson-compounding it, gives rise to the discrete-stable distribution of Steutel and van Harn. We first address the question of the discrete self-decomposability of Sibuya and Sibuya-related distributions. Discrete self-decomposable distributions a...
Article
Take a complete (sub-)critical Galton-Watson branching tree with finitely many leaves almost surely. Picking two distinct leaves at random, we ask for the height (as measured from the root) of their latest common ancestor. Upon conditioning on the first branching event we compute the distribution of this height, with calculations explicit in the ca...
Article
Scientists reinvent stochastic mechanisms leading to the emergence of a distribution discovered by H.A. Simon, in the context of the study of word frequencies occurring in a textbook. Simon distributions are heavy-tailed as a result of a reinforcement mechanism that produced them, related to the modern notion of preferential attachment. The Simon d...
Article
Full-text available
Some population is made of n individuals that can be of p possible species (or types). The update of the species abundance occupancies is from a Moran mutational model designed by Karlin and McGregor in 1967. We first study the equilibrium species counts as a function of n, p and the total mutation probability ν\documentclass[12pt]{minimal} \usepac...
Article
Full-text available
The distributions of the times to the first common ancestor t_mrca is numerically studied for an ecological population model, the extended Moran model. This model has a fixed population size N. The number of descendants is drawn from a beta distribution Beta(alpha, 2-alpha) for various choices of alpha. This includes also the classical Moran model...
Article
Full-text available
We revisit the main features of the Bagchi-Pal urn process as a skewed urn scheme with persistence effects, sometimes emphasizing the specificities of its Pólya-Friedman symmetric version. The Bagchi-Pal scheme is an urn model with two types of balls and iterative replacement of balls obeying positive balance and tenability conditions. Interest is...
Article
Full-text available
Copulas offer a very general tool to describe the dependence structure of random variables supported by the hypercube. Inspired by problems of species abundances in Biology, we study three distinct toy models where copulas play a key role. In a first one, a Marshall–Olkin copula arises in a species extinction model with catastrophe. In a second one...
Article
Full-text available
The shape of a drop pinned in a local equilibrium on an incline is a long-standing problem. The substrate can be homogeneous or heterogeneous and we herewith consider a drop pinned on an incline at the junction between a hydrophilic half-plane (the top half) and a hydropho-bic one (the bottom half). Relying on the equilibrium equations deriving fro...
Article
Full-text available
We first revisit the multi-allelic mutation-fitness balance problem , especially when mutations obey a house of cards condition, where the discrete-time deterministic evolutionary dynamics of the allelic frequencies derives from a Shahshahani potential. We then consider multi-allelic Wright-Fisher stochastic models whose deviation to neutrality is...
Technical Report
Full-text available
The Luria-Delbrück model essentially deals with an intertwining of a two-types process (sensitive against mutants), whereby individual resistant mutants collectively emerge randomly and grow or die at birth events sustained by an exponentially growing sensitive population. We revisit this classical problem and investigate new scenarii involving (su...
Article
Full-text available
After an introduction to the general topic of models for a given locus of a diploid population whose quadratic dynamics is determined by a fitness landscape, we consider more specifically the models that can be treated using genetic (or train) algebras. In this case, any quadratic offspring inter- action can produce any type of offspring and after...
Article
We revisit some problems arising in the context of multiallelic discrete-time and deterministic evolutionary dynamics driven first by fitness differences and then by segregation distortion. In the model with fitness, we describe classes of fitness matrices exhibiting polymorphism. In the segregation case, still in search for conditions of polymorph...
Article
Full-text available
For a drop on an incline with small tilt angle or small Bond number, when the contact line is a circle, we show that the retentive force factor is exactly pi/2 at first order in the tilt angle or the Bond number. The retentive force factor is the ratio between the weight component along the slope and a capillary force defined as surface tension tim...
Article
Full-text available
We first recall some basic facts from the theory of discrete-time Markov chains arising from two types neutral and non-neutral evolution models of population genetics with constant size. We then define and analyse a version of such models whose fluctuating total population size is conserved on average only. In our model, the population of interest...
Article
Full-text available
Motivated by issues arising in population dynamics, we consider the problem of iterating a given analytic function a number of times. We use the celebrated technique known as Carleman linearization that turns (for a certain class of functions) this problem into simply taking the power of a real number. We expand this method, showing in particular t...
Article
Full-text available
In the theory of finite discrete-time birth and death chains with absorbing endpoint boundaries, the evaluation of both additive and multiplicative path functionals is made possible by their Green and λ–potential kernels. These computations are addressed in the context of such Markov chains. The application to the neutral Moran model of population...
Article
Full-text available
Coalescence processes have received a lot of attention in the context of conditional branching processes with fixed population size and non-overlapping generations. Here we focus on similar problems in the context of the standard unconditional Bienaym\'{e}-Galton-Watson branching processes, either (sub)-critical or supercritical. Using an analytica...
Article
Full-text available
This work addresses several aspects and extensions of the deter- ministic Leslie model, as a matrix-driven demographic evolution of an age- structured population. We first point out its duality with another matrix model, related to backward/forward in time ways of counting individuals. Then, in some special cases, we design explicitly both the eige...
Article
Full-text available
We first recall some basic facts from the theory of discrete-time Markov chains arising from two types neutral and non-neutral evolution models of population genetics with constant size. We then define and analyse a version of such models whose fluctuating total population size is conserved on average only. In our model, the population of interest...
Article
Full-text available
We define and analyze a coalescent process as a recursive box-filling process whose genealogy is given by an ancestral time-reversed, time-inhomogeneous Bienyamé-Galton-Watson process. Special interest is on the expected size of a typical box and its probability of being empty. Special cases leading to exact asymptotic computations are investigated...
Article
Full-text available
We derive some additional results on the Bienyam\'e-Galton-Watson branching process with $\theta -$linear fractional branching mechanism, as studied in \cite{Sag}. This includes: the explicit expression of the limit laws in both the sub-critical cases and the super-critical cases with finite mean, the long-run behavior of the population size in the...
Article
Full-text available
Deterministic population growth models with power-law rates can exhibit a large variety of growth behaviors, ranging from algebraic, exponential to hyperexponential (finite time explosion). In this setup, selfsimilarity considerations play a key role, together with two time substitutions. Two stochastic versions of such models are investigated, sho...
Article
Full-text available
Random variables with Mittag-Leffler distribution can take values either in the set of non-negative integers or in the positive real line. There can be of two different types, one (type-1) heavy-tailed with index α ∈ (0, 1), the other (type-2) possessing all its moments. We investigate various stochastic processes where they play a key role, among...
Article
We consider a restricted Solid-on-Solid interface in \(\mathbb {Z}_{+}\), subject to a potential \(V\left( n\right) \) behaving at infinity like \(-\text {w} /n^{2}\). Whenever there is a wetting transition as \(b_{0}\equiv \exp V\left( 0\right) \) is varied, we prove the following results for the density of returns \(m\left( b_{0}\right) \) to the...
Research
Full-text available
The theory of finite discrete-time transient birth and death chains with absorbing endpoint boundaries shows how important it is to compute the Green kernels of such models. We investigate this question in this general context in a first introductory part. As a first illustration, we apply our findings to the neutral Moran model of population genet...
Article
Preface to the special issue on Extreme Events and its Applications.
Data
Revised version of: 'On the spread of a branching Brownian motion whose offspring number has infinite variance', with a different title.
Article
Full-text available
This paper is an attempt to formalize analytically the question raised in "World Population Explained: Do Dead People Outnumber Living, Or Vice Versa?" Huffington Post, \cite{HJ}. We start developing simple deterministic Malthusian growth models of the problem (with birth and death rates either constant or time-dependent) before running into both l...
Article
We study the impact of having a non-spatial branching mechanism with infinite variance on some parameters (height, width and first hitting time) of an underlying Bienaymé–Galton–Watson branching process. Aiming at providing a comparative study of the spread of an epidemics whose dynamics is given by the modulus of a branching Brownian motion (BBM)...
Article
Full-text available
Compound Poisson population models are particular conditional branching process models. A formula for the transition probabilities of the backward process for general compound Poisson models is verified. Symmetric compound Poisson models are defined in terms of a parameter θ ∈ (0, ∞) and a power series φ with positive radius r of convergence. It is...
Article
Full-text available
We show that a two-scale model in 1+1 dimensions enhances su-perhydrophobicity. The two scales may differ by a factor of order two or three, or by a large factor in a scaling limit. In both cases, we compute explictly the macroscopic contact angles as function of the flat material contact angle and aspect ratios. In addition to the Cassie-Baxter st...
Technical Report
Full-text available
We consider a restricted Solid-on-Solid interface in Z_+, subject to a potential V(n) behaving at infinity like -w/n^2. Whenever there is a wetting transition as b_0=exp V(0) is varied, we prove the following results for the density of returns m(b_0) to the origin: If w<-3/8, then m(b_0) has a jump at b_0^c; if -3/8<w<1/8, then m(b_0)~(b_0^c-b_0)^{...
Article
Full-text available
We study duality relations for zeta and M\"{o}bius matrices and monotone conditions on the kernels. We focus on the cases of family of sets and partitions. The conditions for positivity of the dual kernels are stated in terms of the positive M\"{o}bius cone of functions, which is described in terms of Sylvester formulae. We study duality under coar...
Article
Full-text available
We study the impact on shape parameters of an underlying Bienaym\'e-Galton-Watson branching process (height, width and first hitting time), of having a non-spatial branching mechanism with infinite variance. Aiming at providing a comparative study of the spread of an epidemics whose dynamics is given by the modulus of a branching Brownian motion (B...
Article
Full-text available
We consider theoretically the Cassie-Baxter and Wenzel states describing the wetting contact angles for rough substrates. More precisely, we consider different types of periodic geometries such as square protrusions and disks in 2D, grooves and nanoparticles in 3D and derive explicitly the contact angle formulas. We also show how to introduce the c...
Article
Full-text available
Estimating the number n of unseen species from a k-sample displaying only p≤k distinct sampled species has received attention for long. It requires a model of species abundance together with a sampling model. We start with a discrete model of iid stochastic species abundances, each with Gibbs-Poisson distribution. A k-sample drawn from the n-specie...
Article
Full-text available
We study a class of coalescents derived from a sampling procedure out of [Formula: see text] i.i.d. Pareto[Formula: see text] random variables, normalized by their sum, including [Formula: see text] -size-biasing on total length effects ([Formula: see text]). Depending on the range of [Formula: see text] we derive the large [Formula: see text] limi...
Article
Full-text available
The Moran model is a discrete-time birth and death Markov chain describing the evolution of the number of type 1 alleles in a haploid population with two alleles whose total size is preserved during the course of evolution. Bias mechanisms such as mutations or selection can affect its neutral dynamics. For the ergodic Moran model with mutations, w...
Article
Full-text available
This work emphasizes the special role played by max-semistable and log-max-semistable distributions as relevant statistical models of various observable and “internal” variables in Physics. Some of their remarkable properties (chiefly self-similarity) are displayed in some detail. One of their characteristic features is a log-periodic variation of...
Data
Full-text available
When the reproduction law of a discrete branching process pre-serving the total size N of a population is 'balanced', scaling limits of the forward and backward in time processes are known to be the Wright-Fisher diffusion and the Kingman coalescent. When the reproduction law is 'unbalanced', depending on extreme repro-duction events occurring eith...
Article
An extended class of "continuously-generated and deterministic" multifractals with some features common to the ones of "random" multifractals is investigated.
Article
Full-text available
We consider a Markov chain model for population growth sub-ject to rare catastrophic events. In this model, the moves of the process are getting algebraically rare (as from x −λ) when the process visits large heights x, and given a move occurs and the height is large, the chain grows by one unit with large probability or undergoes a rare catastroph...
Article
Full-text available
We study the asymptotics of the extended Moran model as the total population size N tends to infinity. Two convergence results are provided, the first result leading to discrete-time limiting coalescent processes and the second result leading to continuous-time limiting coalescent processes. The limiting coalescent processes allow for multiple merg...
Article
Full-text available
We consider diffusion processes x t on the unit interval. Doobtransformation techniques consist of a selection of x t - paths procedure. The law of the transformed process is the one of a branching diffusion system of particles, each diffusing like a new process x ˜ t , superposing an additional drift to the one of x t . Killing and/or branching of...
Article
Full-text available
Discrete population genetics models with unequal fertilities are considered, with an emphasis on skewed Cannings models, skewed conditional branching process models in the spirit of Karlin and McGregor, and skewed compound Poisson models. Three particular classes of models with skewed fertilities are investigated, the skewed Wright-Fisher model, th...
Article
Full-text available
Consider N equally spaced points on a circle of circumference N. Pick at random n points out of N on this circle and consider the discrete random spacings between consecutive sampled points, turning clockwise. This defines in the first place a random partitioning of N into n positive summands. Append then clockwise an arc of integral length k to ea...
Article
We supply some relations that establish intertwining from duality and give a probabilistic interpretation. This is carried out in the context of discrete Markov chains, fixing up the background of previous relations established for monotone chains and their Siegmund duals. We revisit the duality for birth-and-death chains and the nonneutral Moran m...
Article
Full-text available
We supply some relations that establish intertwining from duality and give a probabilistic interpretation. This is carried out in the context of discrete Markov chains, fixing up the background of previous relations established for monotone chains and their Siegmund duals. We revisit the duality for birth-and-death chains and the nonneutral Moran m...
Article
Full-text available
Consider a droplet of liquid on top of a grooved substrate. The wetting or not of a groove implies the crossing of a potential barrier as the interface has to distort, to hit the bottom of the groove. We start with computing the free energies of the dry and wet states in the context of a simple thermodynamical model before switching to a random mic...
Article
Full-text available
The goal of this manuscript is a comparative study of two Wright-Fisher-like diffusion processes on the interval, one due to Karlin and the other one due to Kimura. Each model accounts for the evolution of one two-locus colony undergoing random mating, under the additional action of selection in random environment. In other words, we study the effe...
Article
Full-text available
We revisit the multi-allelic mutation-fitness balance problem especially when fitnesses are multiplicative. Using ideas arising from quasi-stationary distributions, we analyze the qualitative differences between the fitness-first and mutation-first models, under various schemes of the mutation pattern. We give some stochastic domination relations b...
Article
Full-text available
We consider nonconservative diffusion processes x t on the unit interval, so with absorbing barriers. Using Doob-transformation techniques involving superharmonic functions, we modify the original process to form a new diffusion process x t ~ presenting an additional killing rate part d > 0 . We limit ourselves to situations for which x t ~ is itse...
Article
Full-text available
We shall first consider the classical neutral Moran model with two alleles whose fate is either to become extinct or to reach fixation. We will study an ergodic version of the Moran model obtained by conditioning it to never hit the boundaries, making use of a Doob transform. We shall call it the recurrent Moran model. We will show that the Siegmun...
Article
We consider the random walk on Z_+={ 0,1,...} , with up and down transition probabilities given the chain is in state x in { 1,2,...} : p_{x}=1/2*( 1-delta /{2x+delta }) and q_{x}=1/2*( 1+delta /{2x+delta }) . Here delta >= -1 is a real tuning parameter. We assume that this random walk is reflected at the origin. For delta >0, the walker is attract...
Article
Full-text available
We revisit some problems arising in the context of multiallelic discrete-time evolutionary dynamics driven by fitness. We consider both the deterministic and the stochastic setups and for the latter both the Wright-Fisher and the Moran approaches. In the deterministic formulation, we construct a Markov process whose Master equation identifies with...
Article
Consider the random Dirichlet partition of the interval into $n$ fragments with parameter $\theta >0$. We recall the unordered Ewens sampling formulae from finite Dirichlet partitions. As this is a key variable for estimation purposes, focus is on the number of distinct visited species in the sampling process. These are illustrated in specific case...
Article
The Dirichlet partition of an interval can be viewed as the generalization of several classical models in ecological statistics. We recall the unordered Ewens sampling formulae -ESF) from finite Dirichlet partitions. As this is a key variable for estimation purposes, focus is on the number of distinct visited species in the sampling process. These...
Article
Full-text available
A Markov chain X with finite state space {0,...,N} and tridiagonal transition matrix is considered, where transitions from i to i-1 occur with probability (i/N)(1-p(i/N)) and transitions from i to i+1 occur with probability (1-i/N)p(i/N). Here p:[0,1]→[0,1] is a given function. It is shown that if p is continuous with p(x)≤p(1) for all x∈[0,1] then...
Article
A Markov chain X with finite state space {0,…, N } and tridiagonal transition matrix is considered, where transitions from i to i -1 occur with probability ( i / N )(1- p (i/ N )) and transitions from i to i +1 occur with probability (1- i / N ) p ( i / N ). Here p :[0,1]→[0,1] is a given function. It is shown that if p is continuous with p ( x )≤...
Article
Full-text available
We consider a drift-reversed version of the celebrated Ehrenfest urn process with N balls. For this `dual' process, the boundaries are assumed to be absorbing and so the killing times at the boundaries play a central role. Three natural conditionings on the fixation/extinction events pertaining to this model are investigated. Some spectral informat...
Article
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The purpose of this Note is twofold: First, we introduce the general formalism of evolutionary genetics dynamics involving fitnesses, under both the deterministic and stochastic setups, and chiefly in discrete-time. In the process, we particularize it to a one-parameter model where only a selection parameter is unknown. Then and in a parallel manne...
Article
Full-text available
We work out some relations between duality and intertwining in the context of discrete Markov chains, fixing up the background of previous relations first established for birth and death chains and their Siegmund duals. In view of the results, the monotone properties resulting from the Siegmund dual of birth and death chains are revisited in some d...
Article
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We consider random walks X_n in Z+, obeying a detailed balance condition, with a weak drift towards the origin when X_n tends to infinity. We reconsider the equivalence in law between a random walk bridge and a 1+1 dimensional Solid-On-Solid bridge with a corresponding Hamiltonian. Phase diagrams are discussed in terms of recurrence versus wetting....
Article
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In this note, we try to analyze and clarify the intriguing interplay between some counting problems related to specific thermalized weighted graphs and random walks consistent with such graphs.
Article
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Discrete ancestral problems arising in population genetics are investigated. In the neutral case, the duality concept has been proved of particular interest in the understanding of backward in time ancestral process from the forward in time branching population dynamics. We show that duality formulae still are of great use when considering discrete...
Article
Full-text available
The Pólya process is an urn scheme arising in the context of contagion spreading. It exhibits unstable persistence effects. The Friedman urn process is dual to the Pólya one with antipersistent stabilizing effects. It appears in a safety campaign problem. A Pólya-Friedman urn process is investigated with a tuning persistence parameter extrapolating...

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