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An averaging process on hypergraphs

Part of: Markov processes

Published online by Cambridge University Press:  29 March 2022

Sam Spiro Open the ORCID record for Sam Spiro [Opens in a new window]
Sam Spiro*
Affiliation:
University of California, San Diego
*
*Postal address: 9500 Gilman Dr, La Jolla, CA 92093. Email: sspiro@ucsd.edu
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Abstract

Consider the following iterated process on a hypergraph H. Each vertex v starts with some initial weight $x_v$ . At each step, uniformly at random select an edge e in H, and for each vertex v in e replace the weight of v by the average value of the vertex weights over all vertices in e. This is a generalization of an interactive process on graphs which was first introduced by Aldous and Lanoue. In this paper we use the eigenvalues of a Laplacian for hypergraphs to bound the rate of convergence for this iterated averaging process.

Keywords

Markov chainspectral gap

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 2 , June 2022 , pp. 495 - 504
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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