Displaying similar documents to “Intermittency and ageing for the symbiotic branching model”

Quenched law of large numbers for branching brownian motion in a random medium

János Engländer (2008)

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

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We study a spatial branching model, where the underlying motion is -dimensional (≥1) brownian motion and the branching rate is affected by a random collection of reproduction suppressing sets dubbed . The main result of this paper is the quenched law of large numbers for the population for all ≥1. We also show that the branching brownian motion with mild obstacles than ordinary branching brownian motion by giving an upper estimate on its speed. When the underlying motion is an arbitrary...

Ageing in the parabolic Anderson model

Peter Mörters, Marcel Ortgiese, Nadia Sidorova (2011)

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

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The parabolic Anderson model is the Cauchy problem for the heat equation with a random potential. We consider this model in a setting which is continuous in time and discrete in space, and focus on time-constant, independent and identically distributed potentials with polynomial tails at infinity. We are concerned with the long-term temporal dynamics of this system. Our main result is that the periods, in which the profile of the solutions remains nearly constant, are increasing linearly...

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...

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...