分支运行和翻滚粒子的极值统计
Extreme value statistics for branching run-and-tumble particles
摘要：
活性物质的极值统计提供了对其独特性质的重要见解。一个相变最近被报道在一个模型的分支运行和翻滚粒子，描述了空间扩展的一个不断发展的群体的活性物质在一维。在“持续”阶段中，颗粒形成宏观鲁棒簇，其作为整体弹道传播，而在“间歇”阶段中，颗粒被隔离。我们的研究集中在这个模型的最右边的位置$x_{\max}(t)$达到的时间$t$的波动。在长时间内，随着菌落逐渐侵入未探测区域，$x_{\max}(t)$的累积概率由行进锋描述。这一转变对这一领域产生了显著影响。在间歇阶段，它在性质上类似于满足Fisher-KPP方程的波前，Fisher-KPP方程描述了非活动分支布朗运动的极值统计。一个显着不同的行为出现在持续阶段，活动赋予了我们精确计算的意想不到的和不寻常的特征。
英文摘要：
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 $x_{\max}(t)$ reached by time $t$ for this model. At long time, as the colony progressively invades the unexplored region, the cumulative probability of $x_{\max}(t)$ 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.
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