# Inés Armendáriz's research while affiliated with Universidad de Buenos Aires and other places

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## Publications (20)

We construct an infinite volume spatial random permutation (X,σ), where X⊂Rd is locally finite and σ:X→X is a permutation, associated to the formal Hamiltonian H(X,σ)=∑x∈X‖x-σ(x)‖2.The measures are parametrized by the point density ρ and the temperature α. Spatial random permutations are naturally related to boson systems through a representation o...

The progress of the SARS-CoV-2 pandemic requires the design of large-scale, cost-effective testing programs. Pooling samples provides a solution if the tests are sensitive enough. In this regard, the use of the gold standard, RT-qPCR, raises some concerns. Recently, droplet digital PCR (ddPCR) was shown to be 10–100 times more sensitive than RT-qPC...

The progress of the SARS-CoV-2 pandemic requires the design of cost-effective testing programs at large scale. To this end, pooling multiple samples can provide a solution. Defining a cost-effective strategy requires the establishment of an efficient deconvolution and re-testing procedure that eventually allows the identifcation of the carrier. Bas...

We iterate Dorfman's pool testing algorithm \cite{dorfman} to identify infected individuals in a large population, a classification problem. This is an adaptive scheme with nested pools: pools at a given stage are subsets of the pools at the previous stage. We compute the mean and variance of the number of tests per individual as a function of the...

We provide two methods to construct zero-range processes with superlinear rates on ${\mathbb Z}^d$. In the first method these rates can grow very fast, if either the dynamics and the initial distribution are translation invariant or if only nearest neigbour translation invariant jumps are permitted, in the one-dimensional lattice. In the second met...

We construct an infinite volume spatial random permutation $(\chi,\sigma)$, where $\chi\subset\mathbb R^d$ is a point process and $\sigma:\chi\to \chi$ is a permutation (bijection), associated to the formal Hamiltonian $ H(\chi,\sigma) = \sum_{x\in \chi} \|x-\sigma(x)\|^2$. The measures are parametrized by the density $\rho$ of points and the tempe...

We study a model of spatial random permutations over a discrete set of points. Formally, a permutation $\sigma$ is sampled proportionally to the weight $\exp\{-\alpha \sum_x V(\sigma(x)-x)\},$ where $\alpha>0$ is the temperature and $V$ is a non-negative and continuous potential. The most relevant case for physics is when $V(x)=\|x\|^2$, since it i...

Zero-range processes with decreasing jump rates are known to exhibit
condensation, where a finite fraction of all particles concentrates on a single
lattice site when the total density exceeds a critical value. We study such a
process on a one-dimensional lattice with periodic boundary conditions in the
thermodynamic limit with fixed, super-critica...

We prove that phase transition occurs in the dilute ferromagnetic nearest-neighbour q-state clock model in ℤd, for every q ≥ 2 and d ≥ 2. This follows from the fact that the Edwards-Sokal random-cluster representation of the clock model stochastically dominates a supercritical Bernoulli bond percolation probability, a technique that has been applie...

We consider Gibbs distributions on the set of permutations of $\mathbb Z^d$
associated to the family of specifications $G_\Lambda^\alpha(\sigma)\sim
\exp(-\alpha H_\Lambda(\sigma))$, with Hamiltonian
$H_\Lambda(\sigma):=\sum_{x\in\Lambda} \|\sigma(x)-x\|^2$, where $\sigma$ is a
permutation, $\Lambda$ a finite region of $\mathbb Z^d$ and $\alpha>0$...

Let $\phi(\beta,q,d)$ be the random-cluster probability associated to the
$q$-state clock model at inverse temperature $\beta$ in dimension $d\ge 2$. We
find $\beta_0(q,d)$ such that for $\beta>\beta_0$ the random cluster measure
$\phi(\beta,q,d)$ stochastically dominates a supercritical Bernoulli bond
percolation measure on $\mathbb{Z}^d$. This pr...

We consider Gibbs distributions on the set of permutations of associated to the Hamiltonian , where is a permutation and is a strictly convex potential. Call finite-cycle those permutations composed by finite cycles only. We give conditions on ensuring that for large enough temperature there exists a unique infinite volume ergodic Gibbs measure con...

We introduce a one-dimensional stochastic system where particles perform independent diffusions and interact through pairwise coagulation events, which occur at a nontrivial rate upon collision. Under appropriate conditions on the diffusion coefficients, the coagulation rates and the initial distribution of particles, we derive a spatially inhomoge...

Zero-range processes with decreasing jump rates exhibit a condensation
transition, where a positive fraction of all particles condenses on a single
lattice site when the total density exceeds a critical value. We study the
onset of condensation, i.e. the behaviour of the maximum occupation number
after adding or subtracting a subextensive excess ma...

It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are distributed when a large deviation of the sum is observed.

We study a nonparametric method for estimating the boundary measure
of a compact body G ⊂ ∝d (the boundary length
when d = 2 and the surface area for d = 3) in the case
when this measure agrees with the corresponding Minkowski content. The estimator we consider
is closely related to the one proposed in Cuevas, Fraiman and
Rodríguez-Casal (2007). Ou...

We study a nonparametric method for estimating the boundary measure of a compact body G ⊂ ℝ
d
(the boundary length when d = 2 and the surface area for d = 3) in the case when this measure agrees with the corresponding Minkowski content. The estimator we consider is closely related to the one proposed in Cuevas, Fraiman and Rodríguez-Casal (2007). O...

We prove a strong form of the equivalence of ensembles for the invariant measures of zero range processes conditioned to a supercritical density of particles. It is known that in this case there is a single site that accomodates a macroscopically large number of the particles in the system. We show that in the thermodynamic limit the rest of the si...

## Citations

... In spite of the abundance of evidence in support of pool testing, from proof of concept (19), statistical (37), simulation (29), and field studies (31,32), recommendations from international health agencies have been non-committal and confusing (17,38). Indeed, it is well established that pool testing could increase cost-efficiency even in populations with a prevalence of infection up to 38% (39), if two-stage Dorfman pooling is used, and up to 10% if binary splitting by halving is used (40). ...

... In [V21], local limits of the trace of the non-interacting Brownian cycle loop soup towards the Brownian interlacement process (a Poisson point process on the set of infinitely long Brownian paths) is proved, which is a non-trivial step towards an understanding of the condensate, but still far away from handling the free energy. Another work in this vein was recently done in [AFY19]. ...

... However, this method has not been widely used due to the limited sensitivity of RT-qPCR in testing samples with low viral loads. It has also been suggested that RT-dPCR may be more effective than RT-qPCR in pooled samples due to its higher sensitivity, specificity, and precision; same-day turnaround time; and relatively low cost (23,164,165). To test the suitability of RT-dPCR for pooling, Martin et al. divided 448 COVID-19 hospital samples into three groups (14 pools of 32 samples/pool, 28 pools of 16 samples/pool, and 56 pools of 8 samples/pool) for RT-dPCR testing and directly compared the results to those of individual testing by RT-qPCR (165). ...

... The surface area is defined as the Minkowski content, which coincides with the normalized Hausdorff measure in regular cases. In this setting the convergence rates of the estimators for surface area of ∂S are derived under different shape assumptions ( Cuevas et al. 2007, Pateiro-López and Rodríguez-Casal 2008, Armendáriz et al. 2009). Trillo et al. (2017) consider the same setting but use a more general notion of surface area. ...

... In passing, we mention, among the recent literature on the 'spontaneous' formation of 'condensation', [3] considers, with respect to a thermodynamic limit in 1D symmetric zerorange models, the evolution of the random 'condensate' in a certain time-scale. In [20], with respect to 1D asymmetric dynamics in a set of L fixed sites, motion of the 'condensate' is described. ...

... We are by no means the first to discuss theoretical applications of cluster algorithms. Many such results are known in the literature including a work of Aizenman [1], following Patrascioiu and Seiler [26], on decay of correlations in Lipschitz spin O(2) models, a work of Burton and Steif [8, Section 2] on characterizing the translation-invariant Gibbs states of a certain subshift of finite type, works of Chayes-Machta [12,13], Chayes [11] and Campbell-Chayes [9] relating phase transitions of spin systems with percolative properties of the graphical representation defined by their cluster algorithm, Sheffield's cluster swapping algorithm [29, Chapter 8] used in the characterization of translation-invariant gradient Gibbs states of random surfaces (see also Van den Berg [35] for a related swapping idea used to study uniqueness of Gibbs measures) and a recent work of Armendáriz, Ferrari and Soprano-Loto [2] on phase transition in the dilute clock model. However, these works mostly make use of ad-hoc transformations suitable to the task at hand and we feel that further emphasis of the unifying framework may still be of interest. ...

... have also been studied. An early result due to Fichtner [24] in 1991, and more recently works by Gandolfo, Ruiz and Ueltschi [25], Betz and Ueltschi [26], Betz [27], Biskup and Richthammer [28] and Armendáriz, Ferrari, Groisman and Leonardi [29], consider these issues when the set of points is fixed as either the regular lattice or a realization of a locally finite point process. It is expected that for dimensions d ≥ 3 there is a critical temperature below which, almost surely on the realization of the point process, a typical infinite volume permutation will contain infinite cycles. ...

... A relevant example is the estimation of the (d − 1)-dimensional measure of ∂S. See Cuevas et al. (2007) , Pateiro-López and Rodríguez- Casal (2008), Armendáriz et al. (2009) and Jiménez and Yukich (2011). In all these references, the sample model is somewhat different from the original simple iid situation mentioned above since the available sample information consists of random points drawn inside and outside S. In some sense, the present paper goes along similar lines in the problem of manifold estimation as our main concern here will be the estimation of the (d − 1)-dimensional measure of a manifold S with dimension (d − 1). ...

... The approach in [28, Thm. 3] makes use of an independence result of a linear fraction of these fringe subtrees, which is deduced by applying the independence of the small jumps [2] in a random walk setting with a unique giant jump. The approach for Theorem 3.3 also builds on an independence result for component sizes, see Lemma 3.5 below, but this main lemma is proved differently, using random walks without giant jumps instead. ...

... Although Coagulation equations with diffusion are already being studied [1] both in discrete ( [11], [4]) and continuous setting ( [11], [5]), as limit of particle system ( [18], [12], [3]) or as regularity of its solution [7]. Little is know about the counterpart (1.1) which capture in detail the more complex motion of rain droplet in the atmosphere and is object of this study. ...