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  • Open Access

Dynamic Redundancy and Mortality in Stochastic Search

Samantha Linn1,* and Aanjaneya Kumar2,3,†

  • *Contact author: s.linn@imperial.ac.uk
  • †Contact author: aanjaneya@santafe.edu
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Phys. Rev. Lett. 137, 097102 – Published 25 August, 2026

DOI: https://doi.org/10.1103/s79q-l1dq

Abstract

Stochastic 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 Letter provides a rigorous foundation for studying first-passage processes with a fluctuating number of searchers, with direct relevance across physical, biological, and algorithmic systems.

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Phys. Rev. Lett. 137, 097102– Published 25 August, 2026
  • Received 22 January 2026
  • Revised 30 April 2026
  • Accepted 21 July 2026
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