Displaying similar documents to “Large deviations for voter model occupation times in two dimensions”

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...

Quantitative recurrence in two-dimensional extended processes

Françoise Pène, Benoît Saussol (2009)

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

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Under some mild condition, a random walk in the plane is recurrent. In particular each trajectory is dense, and a natural question is how much time one needs to approach a given small neighbourhood of the origin. We address this question in the case of some extended dynamical systems similar to planar random walks, including ℤ-extension of mixing subshifts of finite type. We define a pointwise recurrence rate and relate it to the dimension of the process, and establish a result of convergence...

Entropy of random walk range

Itai Benjamini, Gady Kozma, Ariel Yadin, Amir Yehudayoff (2010)

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

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We study the entropy of the set traced by an -step simple symmetric random walk on ℤ. We show that for ≥3, the entropy is of order . For =2, the entropy is of order /log2. These values are essentially governed by the size of the boundary of the trace.

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...