Related papers: Transient random walk in symmetric exclusion: limi…

The random walk in Dirichlet environment is a random walk in random environment where the transition probabilities are independent Dirichlet random variables. This random walk exhibits a property of statistical invariance by time-reversal…

We consider a model of random walk in ${\mathbb Z}^2$ with (fixed or random) orientation of the horizontal lines (layers) and with non constant iid probability to stay on these lines. We prove the transience of the walk for any fixed…

We study continuous-time (variable speed) random walks in random environments on $\mathbb{Z}^d$, $d\ge2$, where, at time $t$, the walk at $x$ jumps across edge $(x,y)$ at time-dependent rate $a_t(x,y)$. The rates, which we assume stationary…

We introduce via perturbation a class of random walks in reversible dynamic environments having a spectral gap. In this setting one can apply the mathematical results derived in http://arxiv.org/abs/1602.06322. As first results, we show…

We study the random walk in random environment on {0,1,2,...}, where the environment is subject to a vanishing (random) perturbation. The two particular cases we consider are: (i) random walk in random environment perturbed from Sinai's…

We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…

We prove strong invariance principle between a transient Bessel process and a certain nearest neighbor (NN) random walk that is constructed from the former by using stopping times. It is also shown that their local times are close enough to…

The special limit of the totally asymmetric zero range process of the low-dimensional non-equilibrium statistical mechanics described by the non-Hermitian Hamiltonian is considered. The calculation of the conditional probabilities of the…

We consider random walks in a balanced random environment in $\mathbb{Z}^d$, $d\geq 2$. We first prove an invariance principle (for $d\ge2$) and the transience of the random walks when $d\ge 3$ (recurrence when $d=2$) in an ergodic…

We have shown that the partition function of the Asymmetric Simple Exclusion Process with open boundaries in a sublattice-parallel updating scheme is equal to that of a two-dimensional one-transit walk model defined on a diagonally rotated…

We establish scaling limits for the random walk whose state space is the range of a simple random walk on the four-dimensional integer lattice. These concern the asymptotic behaviour of the graph distance from the origin and the spatial…

The involution walk is the random walk on $S_n$ generated by involutions with a binomially distributed with parameter $1-p$ number of $2$-cycles. This is a parallelization of the transposition walk. The involution walk is shown in this…

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…

A zero-one law of Engelbert--Schmidt type is proven for the norm process of a transient random walk. An invariance principle for random walk local times and a limit version of Jeulin's lemma play key roles.

In this paper we introduce the notion of Random Walk in Changing Environment - a random walk in which each step is performed in a different graph on the same set of vertices, or more generally, a weighted random walk on the same vertex and…

We study a one-dimensional random walk whose expected drift depends both on time and the position of a particle. We establish a non-trivial phase transition for the recurrence vs. transience of the walk, and show some interesting…

We consider random walks in a random environment that is given by i.i.d. Dirichlet distributions at each vertex of Z^d or, equivalently, oriented edge reinforced random walks on Z^d. The parameters of the distribution are a 2d-uplet of…

In this article, a localisation result is proved for the biased random walk on the range of a simple random walk in high dimensions (d \geq 5). This demonstrates that, unlike in the supercritical percolation setting, a slowdown effect…

Using the technique of evolving sets, we explore the connection between entropy growth and transience for simple random walks on connected infinite graphs with bounded degree. In particular we show that for a simple random walk starting at…

Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…