Dresden 2026 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 7: Focus Session: Large Deviations and Rare Events I
DY 7.2: Talk
Monday, March 9, 2026, 10:00–10:15, ZEU/0114
Rare Events, Many Searchers, and Fast Target Reaching in a Finite Domain — Elisabetta Ellettari1, Giacomo Nasuti1, •Alberto Bassanoni1,2, Alessandro Vezzani1,3, and Raffaella Burioni1,2 — 1University of Parma, Italy — 2INFN, Parma associated group, Italy — 3IMEM-CNR, Parma, Italy
Finding a target in a complex environment is a fundamental challenge in nature. An effective strategy to reduce the time needed to reach a target is to deploy many searchers, increasing the likelihood that at least one will succeed by using the statistics of rare events. When the underlying stochastic process involves broadly distributed step sizes, rare long jumps dominate the dynamics, making the use of multiple searchers particularly powerful. We investigate the statistics of extreme events for the mean first passage time in a system of N independent walkers moving with jumps distributed according to a power law, where target-reaching is governed by single, large fluctuations. We show that the mean first passage time of the fastest walker scales as ⟨ τN ⟩ ∼ 1/N, representing a dramatic speed-up compared to classical Brownian search strategies. We derive a scaling law relating the number of walkers required to reach a target within a given time to the size X of the search region. As an application, we model biological fertilization, predicting how the optimal number of spermatozoa scales with uterus size across species. Our predictions match empirical data, and this theory applies broadly to any population of searchers operating within a region of size X, providing a universal framework for efficient search in disordered environments.
Keywords: rare events; first passage time; big jump