Related papers: Limiting velocity of high-dimensional random walk …

We consider several variants of a class of random walks whose increment distributions depend on the average value of the process over its most recent $N$ steps. We investigate the speed of the process, and in particular, the limiting speed…

This paper studies particle propagation in a one-dimensional inhomogeneous medium where the laws of motion are generated by chaotic and deterministic local maps. Assuming that the particle's initial location is random and uniformly…

Symmetric heavily tailed random walks on $Z^d, d\geq 1,$ are considered. Under appropriate regularity conditions on the tails of the jump distributions, global (i.e., uniform in $x,t, |x|+t\to\infty,$) asymptotic behavior of the transition…

We consider a random walk on a multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death. We introduce an auxiliary "core" process that has a regenerative…

One-parameter family of discrete-time quantum-walk models on the square lattice, which includes the Grover-walk model as a special case, is analytically studied. Convergence in the long-time limit $t \to \infty$ of all joint moments of two…

We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. When $d \ge 3$ and the fluctuation of the environment is well moderated by the random walk, we prove a central limit…

We prove large-time $L^2$ and distributional limit theorems for perimeter and diameter of the convex hull of $N$ trajectories of planar random walks whose increments have finite second moments. Earlier work considered $N \in \{1,2\}$ and…

The integer points (sites) of the real line are marked by the positions of a standard random walk. We say that the set of marked sites is weakly, moderately or strongly sparse depending on whether the jumps of the standard random walk are…

We introduce a new self-interacting random walk on the integers in a dynamic random environment and show that it converges to a pure diffusion in the scaling limit. We also find a lower bound on the diffusion coefficient in some special…

We outline basic properties of a symmetric random walk in one dimension, in which the length of the nth step equals lambda^n, with lambda<1. As the number of steps N-->oo, the probability that the endpoint is at x, P_{lambda}(x;N),…

We consider a one-dimensional recurrent random walk in random environment (RWRE). We show that the - suitably centered - empirical distributions of the RWRE converge weakly to a certain limit law which describes the stationary distribution…

We consider biased random walk among iid, uniformly elliptic conductances on $\mathbb{Z}^d$, and investigate the monotonicity of the velocity as a function of the bias. It is not hard to see that if the bias is large enough, the velocity is…

We consider a finite range symmetric exclusion process on the integer lattice in any dimension. We interpret it as a non-elliptic time-dependent random conductance model by setting conductances equal to one over the edges with end points…

A simple symmetric random walk in the space $\mathbb{Z}^2$ is considered. The asymptotic behavior as the number of jumps tends to infinity of the probability that a fixed edge of the random walk lies in the polygon that forms the boundary…

We prove a quenched central limit theorem for balanced random walks in time dependent ergodic random environments which is not necessarily nearest-neigbhor. We assume that the environment satisfies appropriate ergodicity and ellipticity…

We sharpen ellipticity criteria for random walks in i.i.d. random environments introduced by Campos and Ram\'{\i}rez which ensure ballistic behavior. Furthermore, we construct new examples of random environments for which the walk satisfies…

We consider a discrete time random walk in a space-time i.i.d. random environment. We use a martingale approach to show that the walk is diffusive in almost every fixed environment. We improve on existing results by proving an invariance…

This paper gives conditions for the rightmost particle in the $n$th generation of a multitype branching random walk to have a speed, in the sense that its location divided by n converges to a constant as n goes to infinity. Furthermore, a…

Focusing on a continuous-time quantum walk on $\mathbb{Z}=\left\{0,\pm 1,\pm 2,\ldots\right\}$, we analyze a probability distribution with which the quantum walker is observed at a position. The walker launches off at a localized state and…

We introduce ellipticity criteria for random walks in i.i.d. random environments under which we can extend the ballisticity conditions of Sznitman's and the polynomial effective criteria of Berger, Drewitz and Ramirez originally defined for…