Persistence exponent for random walk on directed versions of $Z^2$

TL;DR

This paper investigates the persistence properties of certain random walks in two-dimensional integer lattices, focusing on the decay rate of the probability that the walk remains positive over time, including models with random environments and orientations.

Contribution

It introduces new results on the persistence exponent for specific classes of random walks in random environments on b2, including those with randomly oriented layers.

Findings

Derived persistence exponents for RWRS in b2.

Analyzed random walks with random orientations of horizontal layers.

Provided insights into the decay behavior of persistence probabilities.

Abstract

We study the persistence exponent for random walks in random sceneries (RWRS) with integer values and for some special random walks in random environment in $\mathbb Z^2$ including random walks in $\mathbb Z^2$ with random orientations of the horizontal layers.