The Axelrod model for the dissemination of culture revisited
type: Item
instance of: scholarly article
title: The Axelrod model for the dissemination of culture revisited
zbMATH Open document ID: 1245.60095
DOI: 10.1214/11-AAP790
published in: The Annals of Applied Probability
publication date: 2012-05-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1004.0365
full work available at URL: https://projecteuclid.org/euclid.aoap/1333372015
review text: The author investigates the Axelrod model, a stochastic process which similarly to the voter model includes social influence but, unlike the voter model, also takes into account homophily. Each vertex of the network of interactions is characterized by a set of \(F\) cultural features, each of which can assume \(q\) states. Pairs of adjacent vertices interact at a rate proportional to the number of features they share, which results in the interacting pair having one more cultural feature in common. The Axelrod model has been extensively studied using numerical simulations and simple mean-field treatments, but analytical results for the spatial model itself are still missing. The author prove analytically for the one-dimensional system convergence to a monocultural equilibrium in terms of clustering when \(F=q=2\), as well as fixation to a highly fragmented configuration when the number of states \(q\) is sufficiently larger as compared with the number of features \(F\). His first result also implies clustering of the one-dimensional constrained voter model.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 91D10
zbMATH DE Number: 6034172
zbMATH Keywords: cultural dynamics
zbMATH Keywords: opinion dynamics
zbMATH Keywords: Axelrod model
zbMATH Keywords: constrained voter model
zbMATH Keywords: social influence
zbMATH Keywords: homophily
author: N. Lanchier
reviewed by: Ivan Křivý
MaRDI profile type: Publication
arXiv ID: 1004.0365
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description: scientific article; zbMATH DE number 6034172