The averaging process on infinite graphs
Gantert, Nina and Vilkas, Timo LU
(2025)
In Alea
22.
p.815-823
- 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:
https://lup.lub.lu.se/record/a24c5b04-6dc3-47cd-9150-5234c1b5edbc
- author
- Gantert, Nina
and Vilkas, Timo
LU
- organization
- publishing date
- 2025
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- 60K35, consensus formation, Edge-averaging process, opinion dynamics
- in
- Alea
- volume
- 22
- pages
- 9 pages
- publisher
- Instituto Nacional de Matematica Pura e Aplicada
- external identifiers
-
- scopus:105013973456
- ISSN
- 1980-0436
- DOI
- 10.30757/ALEA.v22-32
- language
- English
- LU publication?
- yes
- id
- a24c5b04-6dc3-47cd-9150-5234c1b5edbc
- date added to LUP
- 2025-11-17 14:13:30
- date last changed
- 2025-11-18 03:51:07
@article{a24c5b04-6dc3-47cd-9150-5234c1b5edbc,
abstract = {{<p>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<sup>2</sup> 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.</p>}},
author = {{Gantert, Nina and Vilkas, Timo}},
issn = {{1980-0436}},
keywords = {{60K35; consensus formation; Edge-averaging process; opinion dynamics}},
language = {{eng}},
pages = {{815--823}},
publisher = {{Instituto Nacional de Matematica Pura e Aplicada}},
series = {{Alea}},
title = {{The averaging process on infinite graphs}},
url = {{http://dx.doi.org/10.30757/ALEA.v22-32}},
doi = {{10.30757/ALEA.v22-32}},
volume = {{22}},
year = {{2025}},
}