First hitting times to intermittent targets

TL;DR

This paper investigates the first hitting times of a Brownian particle to targets that switch between visible and hidden states, revealing a novel power-law regime in the hitting time distribution under high crypticity conditions.

Contribution

It introduces a stochastic switching model for target visibility and uncovers a new power-law regime in first hitting time statistics, extending classical results.

Findings

Power-law regime emerges at high crypticity.

Asymptotic mapping to Robin boundary conditions.

Results extend to non-Markov and anomalous diffusion cases.

Abstract

In noisy environments such as the cell, many processes involve target sites that are often hidden or inactive, and thus not always available for reaction with diffusing entities. To understand reaction kinetics in these situations, we study the first hitting time statistics of a Brownian particle searching for a target site that switches stochastically between visible and hidden phases. At high crypticity, an unexpected rate limited power-law regime emerges for the first hitting time density, which markedly differs from the classic $t^{-3/2}$ scaling for steady targets. Our problem admits an asymptotic mapping onto a mixed, or Robin, boundary condition. Similar results are obtained with non-Markov targets and particles diffusing anomalously.