Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel–Leader graphs
Sara Brofferio, Wolfgang Woess (2005)
Annales de l'I.H.P. Probabilités et statistiques
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Sara Brofferio, Wolfgang Woess (2005)
Annales de l'I.H.P. Probabilités et statistiques
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François Simenhaus (2007)
Annales de l'I.H.P. Probabilités et statistiques
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Jean-Christophe Mourrat (2011)
Annales de l'I.H.P. Probabilités et statistiques
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Attributing a positive value to each ∈ℤ, we investigate a nearest-neighbour random walk which is reversible for the measure with weights ( ), often known as “Bouchaud’s trap model.” We assume that these weights are independent, identically distributed and non-integrable random variables (with polynomial tail), and that ≥5. We obtain the quenched subdiffusive scaling limit of the model, the limit being the fractional kinetics process. We begin our proof...
Zachary, Stan, Foss, S.G. (2006)
Sibirskij Matematicheskij Zhurnal
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F. den Hollander, R. S. dos Santos (2014)
Annales de l'I.H.P. Probabilités et statistiques
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We prove a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof uses a coupling argument based on the observation that the random walk eventually gets trapped inside the union of space–time cones contained in the infection clusters generated by single infections. In the case where the local drifts of the random walk are smaller than the speed at which infection clusters grow, the...
Martin P. W. Zerner (2000)
Annales de l'I.H.P. Probabilités et statistiques
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Guillotin-Plantard, Nadine, Le Ny, Arnaud (2008)
Electronic Communications in Probability [electronic only]
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