Fixation and consensus times on a network: a unified approach
Abstract
We investigate a set of stochastic models of biodiversity, population genetics, language evolution and opinion dynamics on a network within a common framework. Each node has a state, 0 < xi < 1, with interactions specified by strengths mij. For any set of mij we derive an approximate expression for the mean time to reach fixation or consensus (all xi=0 or 1). Remarkably in a case relevant to language change this time is independent of the network structure.
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