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The averaging process on infinite graphs

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Bibliographic Details
Title: The averaging process on infinite graphs
Authors: Gantert, Nina, Vilkas, Timo
Contributors: Lund University, Lund University School of Economics and Management, LUSEM, Department of Statistics, Lunds universitet, Ekonomihögskolan, Statistiska institutionen, Originator
Source: Alea. 22:815-823
Subject Terms: Natural Sciences, Mathematical Sciences, Probability Theory and Statistics, Naturvetenskap, Matematik, Sannolikhetsteori och statistik
Description: We consider the averaging process on an infinite connected graph with bounded degree and independent, identically distributed starting values or initial opinions. Assuming that the law of the initial opinion of a vertex has a finite second moment, we show that the opinions of all vertices converge in L2 to the first moment of the law of the initial opinions. A key tool in the proof is the Sharing a drink procedure introduced by Olle Häggström.
Access URL: https://doi.org/10.30757/ALEA.v22-32
Database: SwePub
Description
Abstract:We consider the averaging process on an infinite connected graph with bounded degree and independent, identically distributed starting values or initial opinions. Assuming that the law of the initial opinion of a vertex has a finite second moment, we show that the opinions of all vertices converge in L2 to the first moment of the law of the initial opinions. A key tool in the proof is the Sharing a drink procedure introduced by Olle Häggström.
ISSN:19800436
DOI:10.30757/ALEA.v22-32