2024/10/02 by Martin R. Evans, Evans, Martin R., Somrita Ray +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · #Diffusion and Search Dynamics #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2410.01941
openalex publication_date 2024/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Resetting has been shown to reduce the completion time for a stochastic process, such as the first passage time for a diffusive searcher to find a target. The time between two consecutive resetting events is drawn from a waiting time distribution ψ(t), which defines the resetting protocol. Previously, it has been shown that deterministic resetting process with a constant time period, referred to as sharp restart, can minimize the mean first passage time to a fixed target. Here we consider the more realistic problem of a target positioned at a random distance R from the resetting site, selected from a given target distribution PT(R). We introduce the notion of a conjugate target distribution to a given waiting time distribution. The conjugate target distribution, PT^*(R), is that PT(R) for which ψ(t) extremizes the mean time to locate the target. In the case of diffusion we derive an explicit expression for P^*T(R) conjugate to a given ψ(t) which holds in arbitrary spatial dimension. Our results show that stochastic resetting prevails over sharp restart for target distributions with exponential or heavier tails.