2020/06/08 by Bertrand Lacroix-A-Chez-Toine, Lacroix-A-Chez-Toine, Bertrand, Asaf Miron +1
Environmental Science · Mathematics · Physics and Astronomy · #Biological Physics (physics.bio-ph) #Ecosystem dynamics and resilience #FOS: Physical sciences #Mathematical Physics (math-ph) #Micro and Nano Robotics #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #cond-mat.stat-mech #math-ph #math.MP #physics.bio-ph
paper · pdf · doi:10.48550/arxiv.2006.04841
14 pages, 6 figures
arxiv created 2020/06/08 · openalex publication_date 2020/06/08 · arxiv updated 2020/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The extreme value statistics of active matter offer significant insight into their unique properties. A phase transition has recently been reported in a model of branching run-and-tumble particles, describing the spatial spreading of an evolving colony of active matter in one-dimension. In a "persistent" phase, the particles form macroscopic robust clusters that ballistically propagate as a whole while in an "intermittent" phase, particles are isolated instead. We focus our study on the fluctuations of the rightmost position xmax(t) reached by time t for this model. At long time, as the colony progressively invades the unexplored region, the cumulative probability of xmax(t) is described by a travelling front. The transition has a remarkable impact on this front. In the intermittent phase it is qualitatively similar to the front satisfying the Fisher-KPP equation, which famously describes the extreme value statistics of the non-active branching Brownian motion. A dramatically different behaviour appears in the persistent phase, where activity imparts the front with unexpected and unusual features which we compute exactly.