Concentrations for the simple random walk in unbounded nonnegative potentials

TL;DR

This paper studies the cost of a simple random walk moving through a landscape with random, unbounded nonnegative potentials, providing concentration inequalities for travel costs in such environments.

Contribution

It introduces new concentration inequalities for the travel cost of simple random walks in unbounded nonnegative potential landscapes.

Findings

Established concentration inequalities for travel costs

Analyzed the impact of unbounded potentials on random walk behavior

Provided theoretical bounds for travel cost deviations

Abstract

We consider the simple random walk in i.i.d. nonnegative potentials on the multidimensional cubic lattice. Our goal is to investigate the cost paid by the simple random walk for traveling from the origin to a remote location in a landscape of potentials. In particular, we obtain concentration inequalities for the travel cost in unbounded nonnegative potentials.