Trapping of a random walk by diffusing traps

TL;DR

This paper develops an analytical method to study how a random walk is trapped by diffusing traps in various dimensions, confirming a specific decay behavior of survival probability and calculating a key constant.

Contribution

It introduces a systematic analytical approach for trapping phenomena and computes the dimension-dependent constant c_d using an epsilon expansion.

Findings

Confirmed the exponential decay of survival probability in trapping scenarios.

Calculated the constant c_d for different dimensions.

Validated phenomenological predictions through analytical methods.

Abstract

We present a systematic analytical approach to the trapping of a random walk by a finite density rho of diffusing traps in arbitrary dimension d. We confirm the phenomenologically predicted e^{-c_d rho t^{d/2}} time decay of the survival probability, and compute the dimension dependent constant c_d to leading order within an eps=2-d expansion.