Fixation in the one-dimensional Axelrod model

Nicolas Lanchier, Stylianos Scarlatos

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The Axelrod model is a spatial stochastic model for the dynamics of cultures which includes two important social factors: social influence, the tendency of individuals to become more similar when they interact, and homophily, the tendency of individuals to interact more frequently with individuals who are more similar. Each vertex of the interaction network is characterized by its culture, a vector of F cultural features that can each assumes q different states. Pairs of neighbors interact at a rate proportional to the number of cultural features they have in common, which results in the interacting pair having one more cultural feature in common. In this article, we continue the analysis of the Axelrod model initiated by the first author by proving that the one-dimensional system fixates when F ≤ cq where the slope satisfies the equation e -c = c. In addition, we show that the two-feature model with at least three states fixates. This last result is sharp since it is known from previous works that the one-dimensional two-feature two-state Axelrod model clusters.

Original languageEnglish (US)
Pages (from-to)2538-2559
Number of pages22
JournalAnnals of Applied Probability
Volume23
Issue number6
DOIs
StatePublished - Dec 2013

Fingerprint

Fixation
One-dimensional Model
Social Influence
Feature Model
Spatial Model
One-dimensional System
Stochastic Model
Slope
Continue
Directly proportional
Model
Vertex of a graph
Interaction
Culture

Keywords

  • Axelrod model
  • Fixation
  • Interacting particle systems
  • Random walks

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Fixation in the one-dimensional Axelrod model. / Lanchier, Nicolas; Scarlatos, Stylianos.

In: Annals of Applied Probability, Vol. 23, No. 6, 12.2013, p. 2538-2559.

Research output: Contribution to journalArticle

Lanchier, Nicolas ; Scarlatos, Stylianos. / Fixation in the one-dimensional Axelrod model. In: Annals of Applied Probability. 2013 ; Vol. 23, No. 6. pp. 2538-2559.
@article{908889848fc545d4b1e0c1a28e3206d2,
title = "Fixation in the one-dimensional Axelrod model",
abstract = "The Axelrod model is a spatial stochastic model for the dynamics of cultures which includes two important social factors: social influence, the tendency of individuals to become more similar when they interact, and homophily, the tendency of individuals to interact more frequently with individuals who are more similar. Each vertex of the interaction network is characterized by its culture, a vector of F cultural features that can each assumes q different states. Pairs of neighbors interact at a rate proportional to the number of cultural features they have in common, which results in the interacting pair having one more cultural feature in common. In this article, we continue the analysis of the Axelrod model initiated by the first author by proving that the one-dimensional system fixates when F ≤ cq where the slope satisfies the equation e -c = c. In addition, we show that the two-feature model with at least three states fixates. This last result is sharp since it is known from previous works that the one-dimensional two-feature two-state Axelrod model clusters.",
keywords = "Axelrod model, Fixation, Interacting particle systems, Random walks",
author = "Nicolas Lanchier and Stylianos Scarlatos",
year = "2013",
month = "12",
doi = "10.1214/12-AAP910",
language = "English (US)",
volume = "23",
pages = "2538--2559",
journal = "Annals of Applied Probability",
issn = "1050-5164",
publisher = "Institute of Mathematical Statistics",
number = "6",

}

TY - JOUR

T1 - Fixation in the one-dimensional Axelrod model

AU - Lanchier, Nicolas

AU - Scarlatos, Stylianos

PY - 2013/12

Y1 - 2013/12

N2 - The Axelrod model is a spatial stochastic model for the dynamics of cultures which includes two important social factors: social influence, the tendency of individuals to become more similar when they interact, and homophily, the tendency of individuals to interact more frequently with individuals who are more similar. Each vertex of the interaction network is characterized by its culture, a vector of F cultural features that can each assumes q different states. Pairs of neighbors interact at a rate proportional to the number of cultural features they have in common, which results in the interacting pair having one more cultural feature in common. In this article, we continue the analysis of the Axelrod model initiated by the first author by proving that the one-dimensional system fixates when F ≤ cq where the slope satisfies the equation e -c = c. In addition, we show that the two-feature model with at least three states fixates. This last result is sharp since it is known from previous works that the one-dimensional two-feature two-state Axelrod model clusters.

AB - The Axelrod model is a spatial stochastic model for the dynamics of cultures which includes two important social factors: social influence, the tendency of individuals to become more similar when they interact, and homophily, the tendency of individuals to interact more frequently with individuals who are more similar. Each vertex of the interaction network is characterized by its culture, a vector of F cultural features that can each assumes q different states. Pairs of neighbors interact at a rate proportional to the number of cultural features they have in common, which results in the interacting pair having one more cultural feature in common. In this article, we continue the analysis of the Axelrod model initiated by the first author by proving that the one-dimensional system fixates when F ≤ cq where the slope satisfies the equation e -c = c. In addition, we show that the two-feature model with at least three states fixates. This last result is sharp since it is known from previous works that the one-dimensional two-feature two-state Axelrod model clusters.

KW - Axelrod model

KW - Fixation

KW - Interacting particle systems

KW - Random walks

UR - http://www.scopus.com/inward/record.url?scp=84888368332&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84888368332&partnerID=8YFLogxK

U2 - 10.1214/12-AAP910

DO - 10.1214/12-AAP910

M3 - Article

VL - 23

SP - 2538

EP - 2559

JO - Annals of Applied Probability

JF - Annals of Applied Probability

SN - 1050-5164

IS - 6

ER -