Diffusion in a wedge geometry: First-Passage Statistics under Stochastic Resetting

TL;DR

This paper investigates how stochastic resetting affects diffusion and first-passage times within a wedge-shaped domain, revealing conditions under which resetting improves absorption rates and escape pathways, supported by theoretical analysis and numerical simulations.

Contribution

It provides a comprehensive analysis of first-passage statistics in a wedge with resetting, deriving explicit formulas and demonstrating how resetting biases escape routes, a novel insight in stochastic process control.

Findings

Resetting enhances absorption in certain wedge geometries.

Explicit formulas for first-passage probabilities and times are derived.

Numerical simulations confirm theoretical predictions.

Abstract

We study the diffusion process in the presence of stochastic resetting inside a two-dimensional wedge of top angle $\alpha$, bounded by two infinite absorbing edges. In the absence of resetting, the second moment of the first-passage time diverges for $\alpha>\pi/4$ while it remains finite for $\alpha<\pi/4$, resulting in an unbounded or bounded coefficient of variation in the respective angular regimes. Upon introducing stochastic resetting, we analyze the first-passage properties in both cases and identify the geometric configurations in which resetting consistently enhances the rate of absorption or escape through the boundaries. By deriving the expressions for the probability currents and conditional first-passage quantities such as splitting probabilities and conditional mean first-passage times, we demonstrate how resetting can be employed to bias the escape pathway through the favorable boundary. Our theoretical predictions are verified through Langevin-type numerical simulations, showing excellent agreement.