Fixation and consensus times on a network: a unified approach

Preprint

5 January 2009

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.0801.3083

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.

Keywords

FIXATION AND CONSENSUS
POPULATION GENETICS
STOCHASTIC MODELS
NETWORK STRUCTURE
UNIFIED APPROACH
CONSENSUS TIMES
BIODIVERSITY
APPROXIMATE

All Related Versions

Version 1, 2008-01-20, ArXiv
Version 2, 2009-01-05, ArXiv
Published version: Physical Review Letters, 101 (25), 258701.

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