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Reaching consensus on a connected graph

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Haslegrave, John and Puljiz, Mate (2017) Reaching consensus on a connected graph. Journal of Applied Probability, 54 (1). pp. 181-198. doi:10.1017/jpr.2016.94 ISSN 0021-9002.

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Official URL: https://doi.org/10.1017/jpr.2016.94

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Abstract

We study a simple random process in which vertices of a connected graph reach consensus through pairwise interactions. We compute outcome probabilities, which do not depend on the graph structure, and consider the expected time until a consensus is reached. In some cases we are able to show that this is minimised by Kn. We prove an upper bound for the case p = 0 and give a family of graphs which asymptotically achieve this bound. In order to obtain the mean of the waiting time we also study a gambler’s ruin process with delays. We give the mean absorption time and prove that it monotonically increases with p ∈ [0, 1/2] for symmetric delays.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Random walks (Mathematics), Stochastic processes, Charts, diagrams, etc., Graph theory.
Journal or Publication Title: Journal of Applied Probability
Publisher: Applied Probability Trust
ISSN: 0021-9002
Official Date: March 2017
Dates:
DateEvent
March 2017Published
4 April 2017Available
18 July 2016Accepted
Volume: 54
Number: 1
Page Range: pp. 181-198
DOI: 10.1017/jpr.2016.94
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access (Creative Commons)
Date of first compliant deposit: 21 July 2016
Date of first compliant Open Access: 8 May 2017
Funder: Seventh Framework Programme (European Commission) (FP7)
Grant number: HIERATIC (316705)
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