Random walks on complex networks with first-passage resetting,Physical Review E

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Random walks on complex networks with first-passage resetting
Physical Review E ( IF 2.2 ) Pub Date : 2021-06-21 , DOI: 10.1103/physreve.103.062132
Feng Huang _{1,

2} , Hanshuang Chen ₃

Affiliation

We study discrete-time random walks on arbitrary networks with first-passage resetting processes. To the end, a set of nodes are chosen as observable nodes, and the walker is reset instantaneously to a given resetting node whenever it hits either of observable nodes. We derive exact expressions of the stationary occupation probability, the average number of resets in the long time, and the mean first-passage time between arbitrary two nonobservable nodes. We show that all the quantities can be expressed in terms of the fundamental matrix

Z = {(I - Q)}^{- 1}

, where

I

is the identity matrix and

Q

is the transition matrix between nonobservable nodes. Finally, we use ring networks, two-dimensional square lattices, barbell networks, and Cayley trees to demonstrate the advantage of first-passage resetting in global search on such networks.

中文翻译：

复杂网络上的随机游走与首段重置

我们研究了具有首段重置过程的任意网络上的离散时间随机游走。最后，选择一组节点作为可观察节点，并且只要它遇到任何一个可观察节点，就会立即将 walker 重置为给定的重置节点。我们推导出平稳占用概率、长时间内平均重置次数以及任意两个不可观察节点之间的平均首次通过时间的精确表达式。我们证明所有的量都可以用基本矩阵表示