Dynamic redundancy and mortality in stochastic search

TL;DR

This paper introduces a comprehensive framework for stochastic search processes with dynamically changing numbers of agents, revealing new insights into search efficiency and connections to stochastic resetting.

Contribution

It develops a general model for search with agents that join and leave, providing exact first-passage time statistics and uncovering novel links to stochastic resetting.

Findings

Exact first-passage time statistics for dynamic search processes

Identification of regimes where DRM search outperforms traditional methods

Universal lower bounds on mean first-passage times in DRM scenarios

Abstract

Search processes are a fundamental part of natural and artificial systems. In such settings, the number of searchers is rarely constant: new agents may be recruited while others can abandon the search. Despite the ubiquity of these dynamics, their combined influence on search efficiency remains unexplored. Here we present a general framework for stochastic search in which independent agents progressively join and leave the process, a mechanism we term dynamic redundancy and mortality (DRM). Under minimal assumptions on the underlying search dynamics, this framework yields exact first-passage time statistics. It further reveals surprising connections to stochastic resetting, including a regime in which the resetting mean first-passage time emerges as a universal lower bound for DRM, as well as regimes in which DRM search is faster. We illustrate our results through a detailed analysis of one-dimensional Brownian DRM search. Altogether, this work provides a rigorous foundation for studying first-passage processes with a fluctuating number of searchers, with direct relevance across physical, biological, and algorithmic systems.