Related papers: Quenched invariance principle for multidimensional…

We study a continuous time random walk X in an environment of dynamic random conductances. We assume that the conductances are stationary ergodic, uniformly bounded and bounded away from zero and polynomially mixing in space and time. We…

We consider a random walk on a random graph $(V,E)$, where $V$ is the set of open sites under i.i.d. Bernoulli site percolation on the multi-dimensional integer set $\mathbf{Z}^d$, and the transition probabilities of the walk are generated…

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…

We prove a quenched local central limit theorem for continuous-time random walks in $\mathbb Z^d, d\ge 2$, in a uniformly-elliptic time-dependent balanced random environment which is ergodic under space-time shifts. We also obtain Gaussian…

This thesis concerns the study of random walks in random environments (RWRE). Since there are two levels of randomness for random walks in random environments, there are two different distributions for the random walk that can be studied.…

We take the point of view of the particle in a multidimensional nearest neighbor random walk in random environment (RWRE). We prove a quenched large deviation principle and derive a variational formula for the quenched rate function. Most…

We study a continuous time random walk $X$ in an environment of i.i.d. random conductances $\mu_e\in[1,\infty)$. We obtain heat kernel bounds and prove a quenched invariance principle for $X$. This holds even when…

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

We establish an invariance principle for a one-dimensional random walk in a dynamical random environment given by a speed-change exclusion process. The jump probabilities of the walk depend on the configuration of the exclusion in a finite…

We prove the almost sure ('quenched') invariance principle for a random walker on an infinite Bernoulli percolation cluster in $\Z^d$ where $d$ is larger or equal than 2.

We consider a simple random walk (dimension one, nearest neighbour jumps) in a quenched random environment. The goal of this work is to provide sufficient conditions, stated in terms of properties of the environment, under which the Central…

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 a random walk on $\R^d$ in a polynomially mixing random environment that is refreshed at each time step. We use a martingale approach to give a necessary and sufficient condition for the almost-sure functional central limit…

We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…

Consider the dynamic environment governed by a Poissonian field of independent particles evolving as simple random walks on $\mathbb{Z}^d$. The random walk on random walks model refers to a particular stochastic process on $\mathbb{Z}^d$…

Random walks in random sceneries (RWRS) are simple examples of stochastic processes in disordered media. They were introduced at the end of the 70's by Kesten-Spitzer and Borodin, motivated by the construction of new self-similar processes…

We prove a strong law of large numbers and an annealed invariance principle for a random walk in a one-dimensional dynamic random environment evolving as the simple exclusion process with jump parameter $\gamma$. First, we establish that if…

We prove a quenched central limit theorem for random walks in i.i.d. weakly elliptic random environments in the ballistic regime. Such theorems have been proved recently by Rassoul-Agha and Sepp\"al\"ainen in [10] and Berger and Zeitouni in…

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 $\omega(\{x,y\})$,…

Unlike classical simple random walks, one-dimensional random walks in random environments (RWRE) are known to have a wide array of potential limiting distributions. Under certain assumptions, however, it is known that CLT-like limiting…