Clustering and coexistence in the one-dimensional vectorial Deffuant model

Nicolas Lanchier, S. Scarlatos

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The vectorial Deffuant model is a simple stochastic process for the dynamics of opinions that also includes a confidence threshold. To understand the role of space in this type of social interactions, we study the process on the onedimensional lattice where individuals are characterized by their opinion - in favor or against - about F different issues and where pairs of nearest neighbors potentially interact at rate one. Potential interactions indeed occur when the number of issues both neighbors disagree on does not exceed a certain confidence threshold, which results in one of the two neighbors updating her opinion on one of the issues both neighbors disagree on (if any). This paper gives sufficient conditions for clustering of the system and for coexistence due to fixation in a fragmented configuration, showing the existence of a phase transition between both regimes.

Original languageEnglish (US)
Pages (from-to)541-564
Number of pages24
JournalAlea
Volume11
Issue number1
StatePublished - 2014

Fingerprint

Coexistence
Confidence
Clustering
Social Interaction
Fixation
Updating
Stochastic Processes
Nearest Neighbor
Exceed
Phase Transition
Configuration
Sufficient Conditions
Interaction
Model

Keywords

  • Annihilating random walks
  • Clustering
  • Coexistence
  • Interacting particle systems

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Clustering and coexistence in the one-dimensional vectorial Deffuant model. / Lanchier, Nicolas; Scarlatos, S.

In: Alea, Vol. 11, No. 1, 2014, p. 541-564.

Research output: Contribution to journalArticle

@article{57f5804cf6cb4df4a4e6993bb07c08a2,
title = "Clustering and coexistence in the one-dimensional vectorial Deffuant model",
abstract = "The vectorial Deffuant model is a simple stochastic process for the dynamics of opinions that also includes a confidence threshold. To understand the role of space in this type of social interactions, we study the process on the onedimensional lattice where individuals are characterized by their opinion - in favor or against - about F different issues and where pairs of nearest neighbors potentially interact at rate one. Potential interactions indeed occur when the number of issues both neighbors disagree on does not exceed a certain confidence threshold, which results in one of the two neighbors updating her opinion on one of the issues both neighbors disagree on (if any). This paper gives sufficient conditions for clustering of the system and for coexistence due to fixation in a fragmented configuration, showing the existence of a phase transition between both regimes.",
keywords = "Annihilating random walks, Clustering, Coexistence, Interacting particle systems",
author = "Nicolas Lanchier and S. Scarlatos",
year = "2014",
language = "English (US)",
volume = "11",
pages = "541--564",
journal = "Alea",
issn = "1980-0436",
publisher = "Instituto Nacional de Matematica Pura e Aplicada",
number = "1",

}

TY - JOUR

T1 - Clustering and coexistence in the one-dimensional vectorial Deffuant model

AU - Lanchier, Nicolas

AU - Scarlatos, S.

PY - 2014

Y1 - 2014

N2 - The vectorial Deffuant model is a simple stochastic process for the dynamics of opinions that also includes a confidence threshold. To understand the role of space in this type of social interactions, we study the process on the onedimensional lattice where individuals are characterized by their opinion - in favor or against - about F different issues and where pairs of nearest neighbors potentially interact at rate one. Potential interactions indeed occur when the number of issues both neighbors disagree on does not exceed a certain confidence threshold, which results in one of the two neighbors updating her opinion on one of the issues both neighbors disagree on (if any). This paper gives sufficient conditions for clustering of the system and for coexistence due to fixation in a fragmented configuration, showing the existence of a phase transition between both regimes.

AB - The vectorial Deffuant model is a simple stochastic process for the dynamics of opinions that also includes a confidence threshold. To understand the role of space in this type of social interactions, we study the process on the onedimensional lattice where individuals are characterized by their opinion - in favor or against - about F different issues and where pairs of nearest neighbors potentially interact at rate one. Potential interactions indeed occur when the number of issues both neighbors disagree on does not exceed a certain confidence threshold, which results in one of the two neighbors updating her opinion on one of the issues both neighbors disagree on (if any). This paper gives sufficient conditions for clustering of the system and for coexistence due to fixation in a fragmented configuration, showing the existence of a phase transition between both regimes.

KW - Annihilating random walks

KW - Clustering

KW - Coexistence

KW - Interacting particle systems

UR - http://www.scopus.com/inward/record.url?scp=85010878296&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85010878296&partnerID=8YFLogxK

M3 - Article

VL - 11

SP - 541

EP - 564

JO - Alea

JF - Alea

SN - 1980-0436

IS - 1

ER -