Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Ergodic behaviour of “signed voter models”

G. Maillard and T.S. Mountford

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Abstract

We answer some questions raised by Gantert, Löwe and Steif (Ann. Inst. Henri Poincaré Probab. Stat. 41 (2005) 767–780) concerning “signed” voter models on locally finite graphs. These are voter model like processes with the difference that the edges are considered to be either positive or negative. If an edge between a site $x$ and a site $y$ is negative (respectively positive) the site $y$ will contribute towards the flip rate of $x$ if and only if the two current spin values are equal (respectively opposed).

Résumé

Nous répondons à des questions soulevées dans le récent papier de Gantert, Löwe et Steif (Ann. Inst. Henri Poincaré Probab. Stat. 41 (2005) 767–780) concernant les modèles du votant “signés” sur des graphes localement finis. Ce sont des processus de type modèle du votant à la différence que chaque arête est considérée comme étant positive ou bien négative. Si une arête entre un site $x$ et un site $y$ est négative (respectivement positive), le site $y$ contribura au taux de flip de $x$ si et seulement si les deux valeurs actuelles des spins sont égales (respectivement opposées).

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 49, Number 1 (2013), 13-35.

Dates
First available in Project Euclid: 29 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1359470124

Digital Object Identifier
doi:10.1214/12-AIHP511

Mathematical Reviews number (MathSciNet)
MR3060146

Zentralblatt MATH identifier
1271.60104

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C22: Interacting particle systems [See also 60K35]
Secondary: 60G50: Sums of independent random variables; random walks 60G60: Random fields 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Particle system Voter model Random walk Coupling

Citation

Maillard, G.; Mountford, T.S. Ergodic behaviour of “signed voter models”. Ann. Inst. H. Poincaré Probab. Statist. 49 (2013), no. 1, 13--35. doi:10.1214/12-AIHP511. https://projecteuclid.org/euclid.aihp/1359470124


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