An averaging process on hypergraphs. (29th June 2022)

• Record Type: Journal Article
• Authors: Spiro, Sam
• Is Part Of: Journal of applied probability. Volume 59:Number 2(2022)
• Page Start: 495
• Page End: 504
• Publication Date: 2022-06-29
• Subjects: Markov chain -- spectral gap; 60J05 -- 60J20; 519.2
• DOI: 10.1017/jpr.2021.67
• Languages: English
• ISSNs: 0021-9002

Abstract

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.