On Brownian exit times from some non-convex domains

TL;DR

This paper investigates the tail probabilities of Brownian exit times from perturbed multi-strip domains, revealing that particles tend to stay longer in these domains compared to regular strips, due to trapped modes.

Contribution

It introduces a new analysis of Brownian exit times in non-convex, perturbed domains, linking probabilistic behavior to waveguide trapped modes.

Findings

Longer tail probabilities in perturbed multi-strips compared to regular strips.

Existence of trapped modes influences Brownian particle behavior.

Perturbations increase the likelihood of extended stays in the domain.

Abstract

We consider the tail probabilities for Brownian exit time from a class of perturbed multi-strips in Euclidean plane. Under some assumptions we prove that the long stays in a perturbed multi-strip are more likely than those in a strip of the same width. This effect is related to the existence of the trapped modes in waveguides.