Random walk hitting times and effective resistance in sparsely connected Erdős‐Rényi random graphs

Sylvester, J. (2021) Random walk hitting times and effective resistance in sparsely connected Erdős‐Rényi random graphs. Journal of Graph Theory, 96(1), pp. 44-84. (doi: 10.1002/jgt.22551)

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Abstract

We prove a bound on the effective resistance R(x,y) between two vertices x, y of a connected graph which contains a suitably well‐connected subgraph. We apply this bound to the Erdős‐Rényi random graph G(n,p) with np n = Ω(log n), proving that R(x,y) concentrates around 1/ d(x) + 1/ d(y), that is, the sum of reciprocal degrees. We also prove expectation and concentration results for the random walk hitting times, Kirchoff index, cover cost, and the random target time (Kemenyʼs constant) on G(n,p) in the sparsely connected regime log + log log log < n n np n ≤ 1/10.

Item Type:Articles
Additional Information:This work was started while I was part of the MASDOC DTC at the University of Warwick, supported by EPSRC grant no. EP/HO23364/1 and ERC starting grant no. 639046 (RGGC). It was completed while I supported by ERC starting grant no. 679660 (DYNAMIC MARCH).
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Sylvester, Dr John
Authors: Sylvester, J.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Journal of Graph Theory
Publisher:Wiley
ISSN:0364-9024
ISSN (Online):1097-0118
Published Online:17 February 2020
Copyright Holders:Copyright © 2020 The Author
First Published:First published in Journal of Graph Theory 96(1): 44-84
Publisher Policy:Reproduced under a Creative Commons License

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