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**The Axelrod model for the dissemination of culture revisited.**
*(English)*
Zbl 1245.60095

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.

Reviewer: Ivan Křivý (Ostrava)

### MSC:

60K35 | Interacting random processes; statistical mechanics type models; percolation theory |

91D10 | Models of societies, social and urban evolution |

### Keywords:

cultural dynamics; opinion dynamics; Axelrod model; constrained voter model; social influence; homophily
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\textit{N. Lanchier}, Ann. Appl. Probab. 22, No. 2, 860--880 (2012; Zbl 1245.60095)

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