Méndez Vicenç, Masó-Puigdellosas Axel, Sandev Trifce, Campos Daniel
Grup de Física Estadística, Departament de Física, Facultat de Ciències, Edifici Cc., Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain.
Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, 1000 Skopje, Macedonia.
Phys Rev E. 2021 Feb;103(2-1):022103. doi: 10.1103/PhysRevE.103.022103.
We investigate the effects of Markovian resetting 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 nonequilibrium 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.
我们研究了马尔可夫重置事件对连续时间随机游走的影响，其中等待时间和跳跃长度是根据幂律概率密度函数分布的随机变量。我们证明了非平衡稳态和有限平均首次到达时间的存在性。然而，最优重置率的存在取决于两个幂律尾部指数之间的特定关系。我们还通过找到最优随机游走（在重置率、初始位置到目标的距离以及特征输运指数方面使平均首次到达时间最小化）来研究搜索效率。
