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)
Text
250807.pdf - Published Version Available under License Creative Commons Attribution. 1MB |
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 |
University Staff: Request a correction | Enlighten Editors: Update this record