Extreme First-Passage Time of Many Interacting Particles
Abstract
Extreme first-passage events are broadly relevant to biological, chemical, and physical processes in which the first successful arrival determines the outcome. Existing theories are largely confined to noninteracting searchers. Interacting extreme-statistics problems are notoriously difficult because correlations destroy probability factorization. We establish a general framework for interacting extreme search. A no-go theorem shows that broad classes of short-range interactions cannot beat the 1/ln N extreme timescale of N independent Brownian searchers, and complementary upper bounds prove that this scale is exact for repulsive interactions. We then identify three sharp mechanisms beyond the logarithmic class and derive a unified interaction-driven acceleration limit. In particular, deterministic pairwise interaction can at most reduce the extreme search time to order 1/N, while stochastic pairwise forcing attains 1/(Nln N). Our results separate acceleration due to statistical redundancy from that generated by coherent many-body transport or amplified fluctuations, deepening our understanding of interacting many-body systems.
Related
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- Upper tail large deviation for the first passage time in the frog model on Zd with d≥ 2
- Interacting particles in random irregular media
- Half-space last passage percolation with inhomogeneous first row
- Fluctuation bounds for rotationally invariant first-passage percolation
BibTeX
@misc{bao2026extreme,
title = {{Extreme First-Passage Time of Many Interacting Particles}},
author = {Ruicheng Bao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.22528},
eprint = {2607.22528},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.22528},
}
RIS
TY - UNPB
TI - Extreme First-Passage Time of Many Interacting Particles
AU - Ruicheng Bao
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2607.22528
UR - https://arxiv.org/abs/2607.22528
AB - Extreme first-passage events are broadly relevant to biological, chemical, and physical processes in which the first successful arrival determines the outcome. Existing theories are largely confined to noninteracting searchers. Interacting extreme-statistics problems are notoriously difficult because correlations destroy probability factorization. We establish a general framework for interacting extreme search. A no-go theorem shows that broad classes of short-range interactions cannot beat the 1/ln N extreme timescale of N independent Brownian searchers, and complementary upper bounds prove that this scale is exact for repulsive interactions. We then identify three sharp mechanisms beyond the logarithmic class and derive a unified interaction-driven acceleration limit. In particular, deterministic pairwise interaction can at most reduce the extreme search time to order 1/N, while stochastic pairwise forcing attains 1/(Nln N). Our results separate acceleration due to statistical redundancy from that generated by coherent many-body transport or amplified fluctuations, deepening our understanding of interacting many-body systems.
ER -