论文标题
在马尔可夫重置下连续时间随机行走
Continuous time random walks under Markovian resetting
论文作者
论文摘要
我们研究了马尔可夫·拉塞塞特事件对连续时间随机步行的影响，在该步行中，等待时间和跳跃长度是根据功率定律概率密度函数分配的随机变量。我们证明存在非平衡固定状态和有限的平均首次到达时间。但是，最佳的复位率的存在基于两个电源法指数之间的特定关系。我们还通过找到最佳随机步行来调查搜索效率，该步行最大程度地减少了平均到达时间的平均到达时间，即重置速率，初始位置到目标的距离和特征运输指数。
We investigate the effects of markovian resseting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power law probability density functions. We prove the existence of a non-equilibrium stationary state and finite mean first arrival time. However, the existence of an optimum reset rate is conditioned to a specific relationship between the exponents of both power law tails. We also investigate the search efficiency by finding the optimal random walk which minimizes the mean first arrival time in terms of the reset rate, the distance of the initial position to the target and the characteristic transport exponents.
