# Random Walk Among Mobile/Immobile Traps: A Short Review

## TL;DR

This paper reviews the classical problem of a random walk among immobile traps and discusses recent developments in models where traps are mobile, highlighting key results and open questions in the field.

## Contribution

It provides a concise review of the well-studied immobile trap problem and introduces recent findings on mobile traps modeled by Poisson systems of random walks.

## Key findings

- Summary of survival probabilities in immobile trap models
- Recent results on mobile trap models with Poisson systems
- Open questions in the study of mobile traps

## Abstract

There have been extensive studies of a random walk among a field of immobile traps (or obstacles), where one is interested in the probability of survival as well as the law of the random walk conditioned on its survival up to time $t$. In contrast, very little is known when the traps are mobile. We will briefly review the literature on the trapping problem with immobile traps, and then review some recent results on a model with mobile traps, where the traps are represented by a Poisson system of independent random walks on ${\mathbb Z}^d$. Some open questions will be given at the end.