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A lecture on the averaging process

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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 vij, and update theirstates according to some specified rule. The averaging process has real-valued states and the rule: upon meeting, the values Xi(t-),Xj (t-) arereplaced by 1/2 (Xi(t-) + Xj (t-)), 1/2 (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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