Speed Function for Biased Random Walks with Traps

TL;DR

This paper derives a simple formula for the speed of a biased random walk on the integer lattice, where the walk experiences site-dependent random trapping times, providing insights into how traps influence the walk's overall speed.

Contribution

The paper introduces a new explicit formula for the speed of biased random walks with site-dependent random trapping times, advancing understanding of trapping effects.

Findings

Derived a simple formula for the walk's speed based on model parameters.

Showed how traps affect the overall movement speed.

Provided analytical tools for studying biased walks with traps.

Abstract

We consider a biased nearest-neighbor random walk on $\Z$ which at each step is trapped for some random time with random, site-dependent mean. We derive a simple formula for the speed function in terms of the model parameters.