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Large deviations for voter model occupation times in two dimensions

G. Maillard;  T. Mountford — 2009

Annales de l'I.H.P. Probabilités et statistiques

We study the decay rate of large deviation probabilities of occupation times, up to time , for the voter model : ℤ×[0, ∞)→{0, 1} with simple random walk transition kernel, starting from a Bernoulli product distribution with density ∈(0, 1). In [ (1988) 401–413], Bramson, Cox and Griffeath showed that the decay rate order lies in [log(), log()]. In this paper, we establish the true decay rates depending on the level. We show that the decay rates are log() when the deviation from ...

Ergodic behaviour of “signed voter models”

G. Maillard;  T. S. Mountford — 2013

Annales de l'I.H.P. Probabilités et statistiques

We answer some questions raised by Gantert, Löwe and Steif ( (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).

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