Related papers: Quenched large deviations for random walk in a ran…

Moderate deviation principles for empirical measure processes associated with weakly interacting Markov processes are established. Two families of models are considered: the first corresponds to a system of interacting diffusions whereas…

We study a continuous-time random walk, $X$, on $\mathbb{Z}^d$ in an environment of dynamic random conductances taking values in $(0, \infty)$. We assume that the law of the conductances is ergodic with respect to space-time shifts. We…

We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…

We prove two Large deviations principles (LDP) in the zone of moderate deviation probabilities. First we establish LDP for the conditional distributions of moderate deviations of empirical bootstrap measures given empirical probability…

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem (LCLT) for non-autonomous dynamical systems. A key advance is the extension of the spectral…

We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails…

In this paper, we reveal the branching structure for a non-homogeneous random walk with bounded jumps. The ladder time $T_1,$ the first hitting time of $[1,\infty)$ by the walk starting from $0,$ could be expressed in terms of a…

We establish a large deviation principle for the empirical measure process associated with a general class of finite-state mean field interacting particle systems with Lipschitz continuous transition rates that satisfy a certain ergodicity…

We consider random walks in Dirichlet environment (RWDE) on $\Z ^d$, for $ d \geq 3 $, in the sub-ballistic case. We associate to any parameter $ (\alpha_1, ..., \alpha_{2d}) $ of the Dirichlet law a time-change to accelerate the walk. We…

In this work, we establish the existence of large deviation principles of random walk in strongly mixing environments. The quenched and annealed rate functions have the same zero set whose shape is either a singleton point or a line…

There is a long history of establishing central limit theorems for Markov chains. Quantitative bounds for chains with a spectral gap were proved by Mann and refined later. Recently, rates of convergence for the total variation distance were…

We study a limit behavior of a sequence of Markov processes (or Markov chains) such that their distributions outside of any neighborhood of a "singular" point attract to some probability law. In any neighborhood of this point the behavior…

We study a class of non-reversible, continuous-time random walks in random environments on $\mathbb{Z}^d$ that admit a cycle representation with finite cycle length. The law of the transition rates, taking values in $[0, \infty)$, is…

We prove results for random walks in dynamic random environments which do not require the strong uniform mixing assumptions present in the literature. We focus on the "environment seen from the walker"-process and in particular its…

Stochastic processes with random reinforced relocations have been introduced in the physics literature to model animal foraging behaviour. Such a process evolves as a Markov process, except at random relocation times, when it chooses a time…

We consider a biased random walk in positive random conductances on $\mathbb{Z}^d$ for $d\geq 5$. In the sub-ballistic regime, we prove the quenched convergence of the properly rescaled random walk towards a Fractional Kinetics.

We investigate the free energy of nearest-neighbor random walks on $\mathbb{Z}^d$, endowed with a drift along the first axis and evolving in a nonnegative random potential given by i.i.d. random variables. Our main result concerns the…

This paper investigates the large deviation problem in the sample path space of the nearest-neighbor random walks on regular trees. We establish the sample path large deviation principle for the law of the distance from a nearest random…

We consider random walks in dynamic random environments which arise naturally as spatial embeddings of ancestral lineages in spatial locally regulated population models. In particular, as the main result, we prove the quenched central limit…

A deterministic walk in a random environment can be understood as a general random process with finite-range dependence that starts repeating a loop once it reaches a site it has visited before. Such process lacks the Markov property. We…