期刊
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
卷 2022, 期 11, 页码 -出版社
IOP Publishing Ltd
DOI: 10.1088/1742-5468/ac9fc7
关键词
first passage; network dynamics; random graphs; networks; stochastic processes
资金
- Israel Science Foundation
- [1682/18]
This study presents analytical results for the distribution of first-passage times of random walks on random regular graphs. The first-passage trajectories can be classified into those following the shortest path and those not following the shortest path.
We present analytical results for the distribution of first-passage (FP) times of random walks (RWs) on random regular graphs that consist of N nodes of degree c > 3. Starting from a random initial node at time t = 0, at each time step t > 1 an RW hops into a random neighbor of its previous node. In some of the time steps the RW may hop into a yet-unvisited node while in other time steps it may revisit a node that has already been visited before. We calculate the distribution P(T (FP) = t) of first-passage times from a random initial node i to a random target node j, where j not equal i. We distinguish between FP trajectories whose backbone follows the shortest path (SPATH) from the initial node i to the target node j and FP trajectories whose backbone does not follow the shortest path ( not sign SPATH). More precisely, the SPATH trajectories from the initial node i to the target node j are defined as trajectories in which the subnetwork that consists of the nodes and edges along the trajectory is a tree network. Moreover, the shortest path between i and j on this subnetwork is the same as in the whole network. The SPATH scenario is probable mainly when the length l ( ij ) of the shortest path between the initial node i and the target node j is small. The analytical results are found to be in very good agreement with the results obtained from computer simulations.
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