dorsal/arxiv
View SchemaDynamic redundancy and mortality in stochastic search
| Authors | Samantha Linn, Aanjaneya Kumar |
|---|---|
| Categories | |
| ArXiv ID | 2601.07096vv2 |
| URL | https://arxiv.org/abs/2601.07096 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
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 \emph{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.
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"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 \\emph{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.",
"arxiv_id": "2601.07096",
"authors": [
"Samantha Linn",
"Aanjaneya Kumar"
],
"categories": [
"cond-mat.stat-mech",
"math.PR",
"physics.data-an",
"physics.soc-ph"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Dynamic redundancy and mortality in stochastic search",
"url": "https://arxiv.org/abs/2601.07096",
"version": "v2"
},
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