相关论文: Ballistic Random Walk in a Random Environment with…

We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. We prove an invariance principle (functional central limit theorem) under almost every fixed environment. The…

We establish a strong law of large numbers for one-dimensional continuous-time random walks in dynamic random environments under two main assumptions: the environment is required to satisfy a decoupling inequality that can be interpreted as…

We study the asymptotic distribution of random walks on $\mathbb Z^d$ ($d\ge1$) in deterministic reversible environments defined by an assignment of a positive conductance to each edge of $\mathbb Z^d$. We identify a deterministic set of…

In this paper we study random walks on dynamical random environments in $1 + 1$ dimensions. Assuming that the environment is invariant under space-time shifts and fulfills a mild mixing hypothesis, we establish a law of large numbers and a…

We are concerned with random walks on $\mathbb{Z}^d$, $d\geq 3$, in an i.i.d. random environment with transition probabilities $\epsilon$-close to those of simple random walk. We assume that the environment is balanced in one fixed…

We study the Ergodic Properties of Random Walks in stationary ergodic environments without uniform ellipticity under a minimal assumption. There are two main components in our work. The first step is to adopt the arguments of Lawler to…

We study a general class of random walks driven by a uniquely ergodic Markovian environment. Under a coupling condition on the environment we obtain strong ergodicity properties for the environment as seen from the position of the walker,…

We study the asymptotic behaviour of random walks in i.i.d. non-elliptic random environments on $\mathbb{Z}^d$. Standard conditions (and proofs) for ballisticity and the central limit theorem require ellipticity. We use oriented percolation…

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…

We characterize ballistic behavior for general i.i.d. random walks in random environments on $\mathbb{Z}$ with bounded jumps. The two characterizations we provide do not use uniform ellipticity conditions. They are natural in the sense that…

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…

In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$.…

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…

This paper states a law of large numbers for a random walk in a random iid environment on ${\mathbb Z}^d$, where the environment follows some Dirichlet distribution. Moreover, we give explicit bounds for the asymptotic velocity of the…

We prove a law of large numbers for certain random walks on certain attractive dynamic random environments when initialised from all sites equal to the same state. This result applies to random walks on $\mathbb{Z}^d$ with $d\geq1$. We…

We study a random walk in random environment on the non-negative integers. The random environment is not homogeneous in law, but is a mixture of two kinds of site, one in asymptotically vanishing proportion. The two kinds of site are (i)…

In this paper, we study random walks evolving on Z in a dynamic random environment that we assume to have time correlations that decrease polynomially fast. We show a law of large numbers by generalizing methods already used for the…

We study the asymptotic behaviour of random walks in i.i.d. random environments on $\Z^d$. The environments need not be elliptic, so some steps may not be available to the random walker. We prove a monotonicity result for the velocity (when…

We prove an invariance principle for continuous-time random walks in a dynamically averaging environment on $\mathbb Z$. In the beginning, the conductances may fluctuate substantially, but we assume that as time proceeds, the fluctuations…

In this brief note, we study the strong law of large numbers for random walks in random scenery. Under the assumptions that the random scenery is non-stationary and satisfies weakly dependent condition with an appropriate rate, we establish…