Related papers: Joint asymptotic behavior of local and occupation …
In the random acceleration process a point particle moving in one dimension is accelerated by Gaussian white noise with zero mean. Although several fundamental statistical properties of the motion have been analyzed in detail, the…
We study an homogeneous irreducible markovian random walk in a square lattice of arbitrary dimension, with an antisymmetric perturbation acting only in one point. We compute exactly spatial correction to the diffusive behaviour in the…
In this paper we study the asymptotic behavior of a random uniform parking function $\pi_n$ of size $n$. We show that the first $k_n$ places $\pi_n(1),\dots,\pi_n(k_n)$ of $\pi_n$ are asymptotically i.i.d. and uniform on $\{1,2,\dots,n\}$,…
In this thesis, we study the Hawking and Unruh effects in time-dependent situations, as registered by localised spacetimes observers in several asymptotic situations. (Full abstract inside document.)
The aim of this article is to prove asymptotic shape theorems for the contact process in stationary random environment. These theorems generalize known results for the classical contact process. In particular, if H_t denotes the set of…
The aim of this paper is to give, using some contiguous relations, the asymptotic behaviour of some linear combination of two symmetric contiguous hypergeometric functions, under some conditions of their parameters.
We study a continuous time random walk on the $d$-dimensional lattice, subject to a drift and an attraction to large clusters of a subcritical Bernoulli site percolation. We find two distinct regimes: a ballistic one, and a subballistic one…
Spatial structure can arise in spatial point process models via a range of mechanisms, including neighbour-dependent directionally biased movement. This spatial structure is neglected by mean-field models, but can have important effects on…
We consider a class of multi-particle reinforced interacting random walks. In this model, there are some (finite or infinite) particles performing random walks on a given (finite or infinite) connected graph, so that each particle has…
We consider a class of jump processes in euclidean space which are associated to a certain non-local symmetric Dirichlet form. We prove a lower bound on the occupation times of sets, and that a support theorem holds for these processes.
Quantum walks subject to decoherence generically suffer the loss of their genuine quantum feature, a quadratically faster spreading compared to classical random walks. This intuitive statement has been verified analytically for certain…
We consider two or more simple symmetric walks on some graphs, e.g. the real line, the plane or the two dimensional comb lattice, and investigate the properties of the distance among the walkers.
We reduce the local limit theorem for a non-compact semisimple Lie group acting on its symmetric space to establishing that a natural operator associated to the measure is quasicompact. Under strong Diophantine assumptions on the underlying…
The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. Here we explore some natural properties in the context of excellent, equidimensional rings containing a field. In addition, we…
We consider a random walk in confined geometry, starting from a site and eventually reaching a target site. We calculate analytically the distribution of the occupation time on a third site, before reaching the target site. The obtained…
We explore some of the connections between the local picture left by the trace of simple random walk on a discrete cylinder with base a d-dimensional torus, d at least 2, of side-length N running for times of order N^{2d} and the model of…
Suppose that S is an asymptotically stable random walk with norming sequence c_{n} and that T_{x} is the time that S first enters (x,\inf), where x\ge 0. The asymptotic behaviour of P(T_0=n) has been described in a recent paper of Vatutin…
We consider three global characteristic times for a one-dimensional Brownian motion $x(\tau)$ in the interval $\tau\in [0,t]$: the occupation time $t_{\rm o}$ denoting the cumulative time where $x(\tau)>0$, the time $t_{\rm m}$ at which the…
To relax the apparent tension between nonlocal hidden variables and relativity, we propose that the observable proper time is not the same quantity as the usual proper-time parameter appearing in local relativistic equations. Instead, the…
We consider $(1+1)$-dimensional directed polymers in a random potential and provide sufficient conditions guaranteeing joint localization. Joint localization means that for typical realizations of the environment, and for polymers started…