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Stochastic resetting and applications
Journal of Physics A: Mathematical and Theoretical ( IF 2.1 ) Pub Date : 2020-04-19 , DOI: 10.1088/1751-8121/ab7cfe
Martin R Evans 1 , Satya N Majumdar 2 , Grgory Schehr 2
Affiliation  

In this topical review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose position is reset randomly in time with a constant rate r , which corresponds to Poissonian resetting, to some fixed point (e.g. its initial position). This simple system already exhibits the main features of interest induced by resetting: (i) the system reaches a nontrivial nonequilibrium stationary state (ii) the mean time for the particle to reach a target is finite and has a minimum, optimal, value as a function of the resetting rate r . We then generalise to an arbitrary stochastic process (e.g. Lévy flights or fractional Brownian motion) and non-Poissonian resetting (e.g. power-law waiting time distribution for intervals between resetting events). We go on to discuss multiparticle systems as well as extended systems, such as fluctuating interfaces, under resetting. We als...

中文翻译:

随机重置和应用

在本主题评估中,我们考虑了重置过程中的随机过程,近年来它引起了很多关注。我们以一个扩散粒子的简单示例开始,该粒子的位置随时间随机以恒定速率r重置为某个固定点(例如,其初始位置),该速率对应于泊松重置。这个简单的系统已经展现出由复位引起的主要关注特征:(i)系统达到非平凡的非平衡稳态(ii)粒子到达目标的平均时间是有限的,并且具有最小,最佳的值,即复位率r的函数。然后,我们概括为任意随机过程(例如Lévy飞行或分数布朗运动)和非泊松重置(例如,重置事件之间间隔的幂律等待时间分布)。我们将继续讨论复位时的多粒子系统以及扩展系统,例如波动的界面。我们也...
更新日期:2020-04-22
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