Optimizing persistent random searches

TL;DR

This paper analyzes a minimal model of persistent random searchers with short-range memory, revealing an optimal persistence length that minimizes search time and highlighting the importance of target distribution in search strategies.

Contribution

It provides an exact calculation of mean first-passage time for persistent random searches, showing the existence of an optimal persistence length and challenging previous assumptions about Levy walks.

Findings

Optimal persistence length minimizes search time.

Persistent random walks outperform Levy walks in certain target distributions.

Target distribution critically influences search efficiency.

Abstract

We consider a minimal model of persistent random searcher with short range memory. We calculate exactly for such searcher the mean first-passage time to a target in a bounded domain and find that it admits a non trivial minimum as function of the persistence length. This reveals an optimal search strategy which differs markedly from the simple ballistic motion obtained in the case of Poisson distributed targets. Our results show that the distribution of targets plays a crucial role in the random search problem. In particular, in the biologically relevant cases of either a single target or regular patterns of targets, we find that, in strong contrast with repeated statements in the literature, persistent random walks with exponential distribution of excursion lengths can minimize the search time, and in that sense perform better than any Levy walk.