论文标题
随机重置的最大和随机步行记录
Maximum and records of random walks with stochastic resetting
论文作者
论文摘要
我们重新审视了具有随机重置的对称随机步行的极端记录的统计数据，并在多个方向上扩展了早期研究。我们提出了一个扩散的缩放制度（具有有限差异的对称步长分布，较弱的重置概率），其中最大步行及其记录的数量直至离散时间$ n $在单个典型轨迹上彼此渐变成比例。他们的分布遵守规模的法律，该法律由共同的两参数缩放函数统治，在半高斯和牙龈定律之间进行了插值。对称指数步长分布和简单的Polya晶格步行的问题的确切解决方案，以及对其他分布的启发式分析，允许对超出扩散扩散缩放制度的极端和记录的几个方面进行定量研究。
We revisit the statistics of extremes and records of symmetric random walks with stochastic resetting, extending earlier studies in several directions. We put forward a diffusive scaling regime (symmetric step length distribution with finite variance, weak resetting probability) where the maximum of the walk and the number of its records up to discrete time $n$ become asymptotically proportional to each other for single typical trajectories. Their distributions obey scaling laws ruled by a common two-parameter scaling function, interpolating between a half-Gaussian and a Gumbel law. The exact solution of the problem for the symmetric exponential step length distribution and for the simple Polya lattice walk, as well as a heuristic analysis of other distributions, allow a quantitative study of several facets of the statistics of extremes and records beyond the diffusive scaling regime.
