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arXiv · 0801.3083

Fixation and consensus times on a network: a unified approach

G. J. Baxter·R. A. Blythe·A. J. McKane
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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 < x_i < 1, with interactions specified by strengths m_{ij}. For any set of m_{ij} we derive an approximate expression for the mean time to reach fixation or consensus (all x_i=0 or 1). Remarkably in a case relevant to language change this time is independent of the network structure.

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BibTeXRIS

G. J. Baxter, R. A. Blythe, A. J. McKane. 2009-01-05. Fixation and consensus times on a network: a unified approach. https://doi.org/10.1103/physrevlett.101.258701

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