Internal DLA in a random environment

Gérard Ben Arous; Jeremy Quastel; Alejandro F. Ramírez

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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...

On consistency of kernel density estimators for randomly censored data : rates holding uniformly over adaptive intervals

Evarist Giné, Armelle Guillou (2001)

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Chung-type functional laws of the iterated logarithm for tail empirical processes

Paul Deheuvels (2000)

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Rates of strong uniform consistency for multivariate kernel density estimators

Evarist Giné, Armelle Guillou (2002)

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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

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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...