Slowdown estimates for one-dimensional random walks in random environment with holding times

TL;DR

This paper analyzes the slowdown probabilities of a biased one-dimensional random walk in a random environment with inhomogeneous jump rates, providing asymptotic decay rates for the probability of slower-than-typical travel speeds.

Contribution

It introduces a model with spatially inhomogeneous jump rates and derives the asymptotic decay rates for slowdown probabilities, extending previous work on random walks in random environments.

Findings

Decay rate of slowdown probability characterized

Asymptotic behavior of slowdown events determined

Model incorporates inhomogeneous jump rates

Abstract

We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We study the probability that the random walk travels slower than its typical speed and determine its decay rate asymptotic.