A lecture on the averaging process

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 ν_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 ½(X_i(t−)+X_j(t−)),½(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.