### Abstract

The Axelrod model is a spatial stochastic model for the dynamics of cultures which, similar to the voter model, includes social influence, but differs from the latter by also accounting for another social factor called homophily, the tendency to interact more frequently with individuals who are more similar. Each individual is characterized by its opinions about a finite number of cultural features, each of which can assume the same finite number of states. Pairs of adjacent individuals interact at a rate equal to the fraction of features they have in common, thus modeling homophily, which results in the interacting pair having one more cultural feature in common, thus modeling social influence. It has been conjectured based on numerical simulations that the one-dimensional Axelrod model clusters when the number of features exceeds the number of states per feature. In this article, we prove this conjecture for the two-state model with an arbitrary number of features.

Original language | English (US) |
---|---|

Pages (from-to) | 3701-3717 |

Number of pages | 17 |

Journal | Stochastic Processes and their Applications |

Volume | 122 |

Issue number | 11 |

DOIs | |

State | Published - Nov 2012 |

### Fingerprint

### Keywords

- Annihilating random walks
- Axelrod model
- Interacting particle systems

### ASJC Scopus subject areas

- Modeling and Simulation
- Statistics and Probability
- Applied Mathematics

### Cite this

*Stochastic Processes and their Applications*,

*122*(11), 3701-3717. https://doi.org/10.1016/j.spa.2012.06.010

**Consensus in the two-state Axelrod model.** / Lanchier, Nicolas; Schweinsberg, Jason.

Research output: Contribution to journal › Article

*Stochastic Processes and their Applications*, vol. 122, no. 11, pp. 3701-3717. https://doi.org/10.1016/j.spa.2012.06.010

}

TY - JOUR

T1 - Consensus in the two-state Axelrod model

AU - Lanchier, Nicolas

AU - Schweinsberg, Jason

PY - 2012/11

Y1 - 2012/11

N2 - The Axelrod model is a spatial stochastic model for the dynamics of cultures which, similar to the voter model, includes social influence, but differs from the latter by also accounting for another social factor called homophily, the tendency to interact more frequently with individuals who are more similar. Each individual is characterized by its opinions about a finite number of cultural features, each of which can assume the same finite number of states. Pairs of adjacent individuals interact at a rate equal to the fraction of features they have in common, thus modeling homophily, which results in the interacting pair having one more cultural feature in common, thus modeling social influence. It has been conjectured based on numerical simulations that the one-dimensional Axelrod model clusters when the number of features exceeds the number of states per feature. In this article, we prove this conjecture for the two-state model with an arbitrary number of features.

AB - The Axelrod model is a spatial stochastic model for the dynamics of cultures which, similar to the voter model, includes social influence, but differs from the latter by also accounting for another social factor called homophily, the tendency to interact more frequently with individuals who are more similar. Each individual is characterized by its opinions about a finite number of cultural features, each of which can assume the same finite number of states. Pairs of adjacent individuals interact at a rate equal to the fraction of features they have in common, thus modeling homophily, which results in the interacting pair having one more cultural feature in common, thus modeling social influence. It has been conjectured based on numerical simulations that the one-dimensional Axelrod model clusters when the number of features exceeds the number of states per feature. In this article, we prove this conjecture for the two-state model with an arbitrary number of features.

KW - Annihilating random walks

KW - Axelrod model

KW - Interacting particle systems

UR - http://www.scopus.com/inward/record.url?scp=84864813857&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864813857&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2012.06.010

DO - 10.1016/j.spa.2012.06.010

M3 - Article

VL - 122

SP - 3701

EP - 3717

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 11

ER -