Internal DLA in a random environment
Gérard Ben Arous, Jeremy Quastel, Alejandro F. Ramírez (2003)
Annales de l'I.H.P. Probabilités et statistiques
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Gérard Ben Arous, Jeremy Quastel, Alejandro F. Ramírez (2003)
Annales de l'I.H.P. Probabilités et statistiques
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C. Landim (1991)
Annales de l'I.H.P. Physique théorique
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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...
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...
Dai Pra, Paolo, Posta, Gustavo (2005)
Electronic Journal of Probability [electronic only]
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Paul Deheuvels (2000)
Annales de l'I.H.P. Probabilités et statistiques
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