Displaying similar documents to “Mixing time for the Ising model : a uniform lower bound for all graphs”

Large deviations for voter model occupation times in two dimensions

G. Maillard, T. Mountford (2009)

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

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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...

On the volume of intersection of three independent Wiener sausages

M. van den Berg (2010)

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

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Let be a compact, non-polar set in ℝ, ≥3 and let ()={ ()+: 0≤≤, ∈} be Wiener sausages associated to independent brownian motions , =1, 2, 3 starting at 0. The expectation of volume of ⋂=13 () with respect to product measure is obtained in terms of the equilibrium measure of in the limit of large .

Annealed vs quenched critical points for a random walk pinning model

Matthias Birkner, Rongfeng Sun (2010)

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

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We study a random walk pinning model, where conditioned on a simple random walk on ℤ acting as a random medium, the path measure of a second independent simple random walk up to time is Gibbs transformed with hamiltonian − (, ), where (, ) is the collision local time between and up to time . This model arises naturally in various contexts, including the study of the parabolic Anderson model with moving catalysts, the parabolic Anderson model with brownian...

Almost-sure growth rate of generalized random Fibonacci sequences

Élise Janvresse, Benoît Rittaud, Thierry de la Rue (2010)

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

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We study the generalized random Fibonacci sequences defined by their first non-negative terms and for ≥1, +2= +1± (linear case) and +2=| +1± | (non-linear case), where each ± sign is independent and either + with probability or − with probability 1− (0<≤1). Our main result is that, when is of the form =2cos(/) for some integer ≥3, the exponential growth of ...

Moderate deviations for a Curie–Weiss model with dynamical external field

Anselm Reichenbachs (2013)

ESAIM: Probability and Statistics

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In the present paper we prove moderate deviations for a Curie–Weiss model with external magnetic field generated by a dynamical system, as introduced by Dombry and Guillotin-Plantard in [C. Dombry and N. Guillotin-Plantard, 15 (2009) 1–30]. The results extend those already obtained for the Curie–Weiss model without external field by Eichelsbacher and Löwe in [P. Eichelsbacher and M. Löwe, 10 (2004) 345–366]. The Curie–Weiss model with dynamical external field is related to the so called...

Disorder relevance for the random walk pinning model in dimension 3

Matthias Birkner, Rongfeng Sun (2011)

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

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We study the continuous time version of the , where conditioned on a continuous time random walk ( )≥0 on ℤ with jump rate > 0, which plays the role of disorder, the law up to time of a second independent random walk ( )0≤≤ with jump rate 1 is Gibbs transformed with weight e (,), where (, ) is the collision local time between and up to time . As the inverse temperature varies, the model undergoes a localization–delocalization...