Probability Surveys

A lecture on the averaging process

David Aldous and Daniel Lanoue

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Abstract

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.

Article information

Source
Probab. Surveys, Volume 9 (2012), 90-102.

Dates
First available in Project Euclid: 23 January 2012

Permanent link to this document
https://projecteuclid.org/euclid.ps/1327328305

Digital Object Identifier
doi:10.1214/11-PS184

Mathematical Reviews number (MathSciNet)
MR2908618

Zentralblatt MATH identifier
1245.60088

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60K99: None of the above, but in this section

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

Citation

Aldous, David; Lanoue, Daniel. A lecture on the averaging process. Probab. Surveys 9 (2012), 90--102. doi:10.1214/11-PS184. https://projecteuclid.org/euclid.ps/1327328305


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