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2012 A lecture on the averaging process
David Aldous, Daniel Lanoue
Probab. Surveys 9: 90-102 (2012). DOI: 10.1214/11-PS184


To interpret interacting particle system style models as social dynamics, suppose each pair {i,j} of individuals in a finite population meet at random times of arbitrary specified rates νij, and update their states according to some specified rule. The averaging process has real-valued states and the rule: upon meeting, the values Xi(t),Xj(t) are replaced by ½(Xi(t)+Xj(t)),½(Xi(t)+Xj(t)). It is curious this simple process has not been studied very systematically. We provide an expository account of basic facts and open problems.


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David Aldous. Daniel Lanoue. "A lecture on the averaging process." Probab. Surveys 9 90 - 102, 2012.


Published: 2012
First available in Project Euclid: 23 January 2012

zbMATH: 1245.60088
MathSciNet: MR2908618
Digital Object Identifier: 10.1214/11-PS184

Primary: 60K35
Secondary: 60K99

Keywords: Duality , interacting particle systems , rate of convergence , spectral gap , voter model

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.9 • 2012
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