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The averaging process on infinite graphs

Gantert, Nina and Vilkas, Timo LU orcid (2024) p.1-11
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.
Please use this url to cite or link to this publication:
author
and
organization
alternative title
Utjämningsprocessen på oändliga grapher
publishing date
type
Working paper/Preprint
publication status
published
subject
keywords
Averaging process, law of large numbers, sharing a drink procedure
pages
11 pages
publisher
arXiv.org
DOI
10.48550/arXiv.2408.06859
language
English
LU publication?
yes
id
382178d2-34f4-41a2-93dc-a265c29592c1
date added to LUP
2025-03-10 10:08:42
date last changed
2025-04-04 14:34:02
@misc{382178d2-34f4-41a2-93dc-a265c29592c1,
  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.}},
  author       = {{Gantert, Nina and Vilkas, Timo}},
  keywords     = {{Averaging process; law of large numbers; sharing a drink procedure}},
  language     = {{eng}},
  month        = {{08}},
  note         = {{Preprint}},
  pages        = {{1--11}},
  publisher    = {{arXiv.org}},
  title        = {{The averaging process on infinite graphs}},
  url          = {{http://dx.doi.org/10.48550/arXiv.2408.06859}},
  doi          = {{10.48550/arXiv.2408.06859}},
  year         = {{2024}},
}