Return probabilities and hitting times of random walks on sparse Erdos-Renyi graphs

TL;DR

This paper analyzes return probabilities and hitting times of random walks on sparse Erdos-Renyi graphs, revealing self-similar distribution patterns using a tree-based approach in the large graph limit.

Contribution

It introduces a tree-based method to exactly compute the distribution of return probabilities and hitting times for sparse Erdos-Renyi graphs in the large graph limit.

Findings

Distributions exhibit self-similarity.

Method provides exact solutions in the large graph limit.

Applicable to sparse Erdos-Renyi graphs.

Abstract

We consider random walks on random graphs, focusing on return probabilities and hitting times for sparse Erdos-Renyi graphs. Using the tree approach which is expected to be exact in the large graph limit, we show how to solve for the distribution of these quantities and we find that these distributions exhibit a form of self-similarity.