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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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).


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

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

First available in Project Euclid: 29 January 2013

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Zentralblatt MATH identifier

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)

Particle system Voter model Random walk Coupling


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.

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