Rank-dependent optimal resetting in multiparticle search

Abstract

In many soft-matter and biological systems, task completion relies on the cumulative arrival of multiple searchers rather than the speed of a single pioneer. The completion kinetics are therefore set not only by the first arrival, but by the full ordered sequence of first-passage times. Here, we determine how stochastic resetting optimizes these ordered arrivals for all arrival ranks. We construct an exact finite-N reference for non-interacting Brownian searchers and obtain the mean ordered first-passage time ⟨ T_(k) ⟩ and its optimal resetting rate r_k^*. For searchers with identical initial conditions, r_k^* increases monotonically with arrival rank and, with increasing population size, approaches the known large-N quantile limit where a finite optimum appears only above a critical rank fraction ϕ_c ≃ 0.412. Spatial heterogeneity qualitatively reorganizes this sequence, shifting its maximum from late to early ranks even without particle interactions. We then compare this baseline with Brownian colloid experiments, interacting active Brownian particles, and a collective autochemotactic search with persistent environmental memory. Across these systems, sensitivity to resetting increases strongly with arrival rank, while deviations from appropriate non-interacting references reveal the influence of direct interactions, finite return overhead, and environmental memory. Our results show that optimal resetting in multiparticle search is governed by the required completion rank and must be evaluated relative to protocol- and geometry-matched baselines.

2D target search with boundary-induced resetting
Kevin Chen, Paul C. Bressloff
arXiv25 Sep 2026PreprintarXiv licenceFull textAnalysis & PDEs ProbabilityarXiv
Optimal Evasion from a Resetting Searcher
Ami Taitelbaum, Matan Shporer, Shlomi Reuveni +1
arXiv23 Sep 2026PreprintarXiv licenceFull textComputational physics Statistical & nonlinear physicsarXiv
Improved nonflow control for multiparticle correlators and system-size-dependent evolution from OO to Pb--Pb collisions at the LHC
Neelkamal Mallick, Suraj Prasad
arXiv27 Oct 2026PreprintCC BY 4.0Full textHigh-energy & particle physics Nuclear physicsarXiv
Optimal Quantum Algorithms for Ordered Search
Joseph Carolan, Andrew M. Childs
arXiv28 Sep 2026PreprintCC BY 4.0Full textQuantum physics & quantum informationarXiv
Optimal low-rank compression of quantum dynamics
Hugo Mackay, Donghoon Kim, Tan Van Vu +1
arXiv23 Sep 2026PreprintCC BY 4.0Full textMathematical physics Condensed matterarXiv

Cite

BibTeX RIS

BibTeX

@misc{vatash2026rankdependent,
  title = {{Rank-dependent optimal resetting in multiparticle search}},
  author = {Ron Vatash and Eden Goldfarb and Vladimir Yu. Rudyak and Yael Roichman},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23542},
  eprint = {2609.23542},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23542},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Rank-dependent optimal resetting in multiparticle search
AU  - Ron Vatash
AU  - Eden Goldfarb
AU  - Vladimir Yu. Rudyak
AU  - Yael Roichman
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23542
UR  - https://arxiv.org/abs/2609.23542
AB  - In many soft-matter and biological systems, task completion relies on the cumulative arrival of multiple searchers rather than the speed of a single pioneer. The completion kinetics are therefore set not only by the first arrival, but by the full ordered sequence of first-passage times. Here, we determine how stochastic resetting optimizes these ordered arrivals for all arrival ranks. We construct an exact finite-N reference for non-interacting Brownian searchers and obtain the mean ordered first-passage time ⟨ T_(k) ⟩ and its optimal resetting rate r_k^*. For searchers with identical initial conditions, r_k^* increases monotonically with arrival rank and, with increasing population size, approaches the known large-N quantile limit where a finite optimum appears only above a critical rank fraction ϕ_c ≃ 0.412. Spatial heterogeneity qualitatively reorganizes this sequence, shifting its maximum from late to early ranks even without particle interactions. We then compare this baseline with Brownian colloid experiments, interacting active Brownian particles, and a collective autochemotactic search with persistent environmental memory. Across these systems, sensitivity to resetting increases strongly with arrival rank, while deviations from appropriate non-interacting references reveal the influence of direct interactions, finite return overhead, and environmental memory. Our results show that optimal resetting in multiparticle search is governed by the required completion rank and must be evaluated relative to protocol- and geometry-matched baselines.
ER  -

Abstract

Related

Cite