The averaging process on infinite graphs

Fuente: arXiv
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Main Authors: Gantert, Nina, Vilkas, Timo
Format: Preprint
Published: 2024
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author Gantert, Nina
Vilkas, Timo
author_facet Gantert, Nina
Vilkas, Timo
contents 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 $L^2$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2408_06859
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The averaging process on infinite graphs
Gantert, Nina
Vilkas, Timo
Probability
60F25, 60K35
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 $L^2$ 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.
title The averaging process on infinite graphs
topic Probability
60F25, 60K35
url https://arxiv.org/abs/2408.06859