TY - JOUR

T1 - Analytical results for the distribution of first-passage times of random walks on random regular graphs

AU - Tishby, Ido

AU - Biham, Ofer

AU - Katzav, Eytan

N1 - Publisher Copyright:
© 2022 IOP Publishing Ltd and SISSA Medialab srl.

PY - 2022/11/1

Y1 - 2022/11/1

N2 - 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 ≠ 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 (¬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.

AB - 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 ≠ 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 (¬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.

KW - first passage

KW - network dynamics

KW - random graphs, networks

KW - stochastic processes

UR - http://www.scopus.com/inward/record.url?scp=85143296152&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/ac9fc7

DO - 10.1088/1742-5468/ac9fc7

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85143296152

SN - 1742-5468

VL - 2022

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 11

M1 - 113403

ER -