Related papers: Reversed Dirichlet environment and directional tra…

We derive a quenched invariance principle for random walks in random environments whose transition probabilities are defined in terms of weighted cycles of bounded length. To this end, we adapt the proof for random walks among random…

Consider a simple random walk on the integers with the following transition mechanism. At each site $x$, the probability of jumping to the right is $\omega(x)\in[\frac12,1)$, until the first time the process jumps to the left from site $x$,…

We look at random walks in Dirichlet environment. It was known that in dimension $d\geq 3$, if the walk is sub-ballistic, the displacement of the walk is polynomial of order $\kappa$ for some explicit $\kappa$. We show that the walk, after…

We study a random walk on $\mathbb{Z}$ which evolves in a dynamic environment determined by its own trajectory. Sites flip back and forth between two modes, $p$ and $q$. $R$ consecutive right jumps from a site in the $q$-mode are required…

The probability that a one dimensional excited random walk in stationary ergodic and elliptic cookie environment is transient to the right (left) is either zero or one. This solves a problem posed by Kosygina and Zerner [8].

We consider random walks in a random environment of the type p_0+\gamma\xi_z, where p_0 denotes the transition probabilities of a stationary random walk on \BbbZ^d, to nearest neighbors, and \xi_z is an i.i.d. random perturbation. We give…

We consider the dynamics of lattice random walks with resetting. The walker moving randomly on a lattice of arbitrary dimensions resets at every time step to a given site with a constant probability $r$. We construct a discrete renewal…

In this note we first consider local times of random walks killed at leaving positive half-axis. We prove that the distribution of the properly rescaled local time at point $N$ conditioned on being positive converges towards an exponential…

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 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…

We consider transient random walks in random environment on Z in the positive speed (ballistic) and critical zero speed regimes. A classical result of Kesten, Kozlov and Spitzer proves that the hitting time of level $n$, after proper…

We study the limit behaviour of a class of random walk models taking values in the $d$-dimensional unit standard simplex, $d\ge 1$, defined as follows. From an interior point $z$, the process chooses one of the $d+1$ vertices of the…

In this paper, we consider random walks in Dirichlet random environment (RWDE) on $\mathbb{Z}^2$. We prove that, if the RWDE is recurrent (which is strongly conjectured when the weights are symmetric), then there does not exist any…

We prove a law of large numbers for random walks in certain kinds of i.i.d. random environments in Z^d that is an extension of a result of Bolthausen, Sznitman and Zeitouni (2003). We use this result, along with the lace expansion for…

We consider the random walk in an \emph{i.i.d.} random environment on the infinite $d$-regular tree for $d \geq 3$. We consider the tree as a Cayley graph of free product of finitely many copies of $\Zbold$ and $\Zbold_2$ and define the…

We study the biased random walk in positive random conductances on $\mathbb {Z}^d$. This walk is transient in the direction of the bias. Our main result is that the random walk is ballistic if, and only if, the conductances have finite…

Consider an arbitrary transient random walk on $\Z^d$ with $d\in\N$. Pick $\alpha\in[0,\infty)$ and let $L_n(\alpha)$ be the spatial sum of the $\alpha$-th power of the $n$-step local times of the walk. Hence, $L_n(0)$ is the range,…

We consider a transient random walk on $Z^d$ which is asymptotically stable, without centering, in a sense which allows different norming for each component. The paper is devoted to the asymptotics of the probability of the first return to…

We consider the motion of a particle on a Galton Watson tree, when the probabilities of jumping from a vertex to any one of its neighbours is determined by a random process. Given the tree, positive weights are assigned to the edges in such…

Random flights in $\mathbb{R}^d,d\geq 2,$ with Dirichlet-distributed displacements and uniformly distributed orientation are analyzed. The explicit characteristic functions of the position $\underline{\bf X}_d(t),\,t>0,$ when the number of…