Related papers: Lyapunov exponents, shape theorems and large devia…
We prove a shape theorem and derive a variational formula for the limiting quenched Lyapunov exponent and the Green's function of random walk in a random potential on a square lattice of arbitrary dimension and with an arbitrary finite set…
We establish large deviation principles and phase transition results for both quenched and annealed settings of nearest-neighbor random walks with constant drift in random nonnegative potentials on $\mathbb Z^d$. We complement the analysis…
We consider the simple random walk on $\mathbb{Z}^d$ evolving in a random i.i.d. potential taking values in $[0,+\infty)$. The potential is not assumed integrable, and can be rescaled by a multiplicative factor $\lambda > 0$. Completing the…
We consider a simple random walk in an i.i.d. non-negative potential on the d-dimensional integer lattice, $d\geq 3$. We study the quenched Lyapunov exponents, and present a probabilistic proof of its continuity when the potentials converge…
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…
We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and…
In the first part of the article our subject of interest is a simple symmetric random walk on the integers which faces a random risk to be killed. This risk is described by random potentials, which in turn are defined by a sequence of…
We consider the simple random walk in i.i.d. nonnegative potentials on the $d$-dimensional cubic lattice $\mathbb{Z}^d$ ($d \geq 1$). In this model, the so-called Lyapunov exponent describes the cost of traveling for the simple random walk…
We consider the simple random walk on Z^d, d > 2, evolving in a potential of the form \beta V, where (V(x), x \in Z^d) are i.i.d. random variables taking values in [0,+\infty), and \beta\ > 0. When the potential is integrable, the…
We consider the solution $u$ to the one-dimensional parabolic Anderson model with homogeneous initial condition $u(0, \cdot) \equiv 1$, arbitrary drift and a time-independent potential bounded from above. Under ergodicity and independence…
We consider the simple random walk on supercritical percolation clusters in the multidimensional cubic lattice. In this model, a quenched large deviation principle holds for the position of the random walk. Its rate function depends on the…
We consider the simple random walk on the $d$-dimensional lattice $\mathbb{Z}^d$ ($d \geq 1$), traveling in potentials which are Bernoulli distributed. The so-called Lyapunov exponent describes the cost of traveling for the simple random…
We study quenched distributions on random walks in a random potential on integer lattices of arbitrary dimension and with an arbitrary finite set of admissible steps. The potential can be unbounded and can depend on a few steps of the walk.…
We study continuous time random walks on $\mathbb{Z}^d$ (with $d \geq 2$) among random conductances $\{ \omega(\{x,y\}) : x,y \in \mathbb{Z}^d\}$ that permit jumps of arbitrary length. The law of the random variables $\omega(\{x,y\})$,…
We consider a random walk in a random potential on a square lattice of arbitrary dimension. The potential is a function of an ergodic environment and some steps of the walk. The potential can be unbounded, but it is subject to a moment…
We prove a {\it{quenched}} large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster on $\Z^d$, $d\geq 2$.. We take the point of view of the moving particle and first prove a quenched LDP for the…
We show quenched large deviations for the simple random walk on a certain class of percolations with long-range correlations. This class contains the supercritical Bernoulli percolations, the model considered by Drewitz, R'ath and…
In this work, we study the large deviation properties of random walk in a random environment on $\mathbb{Z}^d$ with $d\geq1$. We start with the quenched case, take the point of view of the particle, and prove the large deviation principle…
We prove a {\it{quenched}} large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on $\mathbb Z^d$ ($d\geq 2$). The models under interest include classical Bernoulli bond and site percolation…
We take the point of view of a particle performing random walk with bounded jumps on $\mathbb{Z}^d$ in a stationary and ergodic random environment. We prove the quenched large deviation principle (LDP) for the pair empirical measure of the…