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 A lecture on the averaging process
 David Aldous, University of California, BerkeleyDaniel Lanoue, University of California, Berkeley

 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 $$\nu_{ij}$$, and update their states according to some specified rule. The averaging process has real-valued states and the rule: upon meeting, the values $$X_i(t-), X_j(t-)$$ are replaced by $$\frac{1}{2}(X_i(t-)+X_j(t-)), \frac{1}{2}(X_i(t-)+X_j(t-))$$. It is curious this simple process has not been studied very systematically. We provide an expository account of basic facts and open problems.AMS 2000 subject classifications: Primary 60K35; secondary 60K99.Keywords: Duality, interacting particle systems, rate of convergence, spectral gap, voter model.
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Aldous, David, Lanoue, Daniel, A lecture on the averaging process, Probability Surveys, 9, (2012), 90-102 (electronic). DOI: 10.1214/11-PS184.

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