论文标题
随机复位的随机步行和Lévy航班的生存概率
Survival probability of random walks and Lévy flights with stochastic resetting
论文作者
论文摘要
我们对具有随机重置的对称随机步行的生存概率进行了彻底的分析，这定义为Walker在$ n $ time $ n $上不跨越原点的概率。对于具有有限的（随机步行）或无限方差（LévyFlights）的步长的连续对称分布，可以用Sparre Andersen理论给出的而无需重置的步行的生存概率来表达此概率。因此，它是通用的，即独立于步长分布。我们分析了深度的生存概率，在有限的时间和渐近的延迟时间结果中得出了确切的结果。我们还研究了步长分布对称但不连续的情况，将注意力集中在算术分布上，在整数的晶格上产生随机步行。我们详细研究了简单的Polya Walk的示例，并提出了一种代数方法，用于较大范围的晶格步道。
We perform a thorough analysis of the survival probability of symmetric random walks with stochastic resetting, defined as the probability for the walker not to cross the origin up to time $n$. For continuous symmetric distributions of step lengths with either finite (random walks) or infinite variance (Lévy flights), this probability can be expressed in terms of the survival probability of the walk without resetting, given by Sparre Andersen theory. It is therefore universal, i.e., independent of the step length distribution. We analyze this survival probability at depth, deriving both exact results at finite times and asymptotic late-time results. We also investigate the case where the step length distribution is symmetric but not continuous, focussing our attention onto arithmetic distributions generating random walks on the lattice of integers. We investigate in detail the example of the simple Polya walk and propose an algebraic approach for lattice walks with a larger range.
