# Gaia Pozzoli's research while affiliated with Università degli Studi dell'Insubria and other places

## Publications (11)

Preprint
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We consider the extreme value statistics of centrally-biased random walks with asymptotically-zero drift in the ergodic regime. We fully characterize the asymptotic distribution of the maximum for this class of Markov chains lacking translational invariance, with a particular emphasis on the relation between the time scaling of the expected value o...
Preprint
We consider a one-dimensional Brownian motion with diffusion coefficient $D$ in the presence of $n$ partially absorbing traps with intensity $\beta$, separated by a distance $L$ and evenly spaced around the initial position of the particle. We study the transport properties of the process conditioned to survive up to time $t$. We find that the surv...
Preprint
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We consider a random walk $Y$ moving on a \emph{L\'evy random medium}, namely a one-dimensional renewal point process with inter-distances between points that are in the domain of attraction of a stable law. The focus is on the characterization of the law of the first-ladder height $Y_{\mathcal{T}}$ and length $L_{\mathcal{T}}(Y)$, where $\mathcal{... Article We consider one-dimensional discrete-time random walks (RWs) in the presence of finite size traps of length ℓ over which the RWs can jump. We study the survival probability of such RWs when the traps are periodically distributed and separated by a distance L . We obtain exact results for the mean first-passage time and the survival probability in t... Preprint We consider one-dimensional discrete-time random walks (RWs) in the presence of finite size traps of length$\ell$over which the RWs can jump. We study the survival probability of such RWs when the traps are periodically distributed and separated by a distance$L\$. We obtain exact results for the mean first-passage time and the survival probabilit...
Article
Full-text available
We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional non-homogeneous random walk with a position-dependent drift known in the mathematical literature as Gillis random walk. This modified stochastic process allows to significantly change local, non-loc...
Preprint
Full-text available
We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional nonhomogeneous random walk with a position-dependent drift known in the mathematical literature as Gillis random walk. This modified stochastic process allows to significantly change local, non-loca...
Article
The Gillis model, introduced more than 60 years ago, is a non-homogeneous random walk with a position-dependent drift. Though parsimoniously cited both in physical and mathematical literature, it provides one of the very few examples of a stochastic system allowing for a number of exact results, although lacking translational invariance. We present...
Preprint
Full-text available
Gillis model, introduced more than 60 years ago, is a non-homogeneous random walk with a position dependent drift. Though parsimoniously cited both in the physical and mathematical literature, it provides one of the very few examples of a stochastic system allowing for a number of exact result, although lacking translational invariance. We present...
Article
We consider the statistics of occupation times, the number of visits at the origin and the survival probability for a wide class of stochastic processes, which can be classified as renewal processes. We show that the distribution of these observables can be characterized by a single exponent, that is connected to a local property of the probability...
Preprint
Full-text available
We consider the statistics of occupation times, the number of visits at the origin and the survival probability for a wide class of stochastic processes, which can be classified as renewal processes. We show that the distribution of these observables can be characterized by a single parameter, that is connected to a local property of the probabilit...

## Citations

... As we emphasized in our previous works [37,39], this random walk is a discrete realization of a diffusing particle in the presence of an asymptotically logarithmic potential. Indeed, if one considers the master equation governing the time evolution of the probability p(j, n) of finding the walker at site j after n steps ...
... For the Gillis model, with a simple computation it is possible to fully determine the stationary distribution [37], which remarkably shows an asymptotic power-law decay where (x) k is the Pochhammer symbol (or rising factorial) and according to the Birkhoff ergodic theorem. In fact, it is easy to observe that in the long-time limit the time average of the number of returns to the origin R n = n k=1 δ X k ,0 converges to the ensemble average of the Kronecker delta, which is π 0 by definition, and at the same time τ is trivially given by the ratio of the number of steps over the mean number of returns R n . ...
... The above mentioned works [16,17] were followed by investigations on the statistics of the occupation time for simpler systems, more amenable to exact analysis, and closer to the main stream of probabilistic studies [19,28,29,30,31,32,33,34]. We refer the reader to [35] for subsequent references and to [36,37,38,39,40,41] for more recent works. ...