Central limit theorem for the excited random walk in dimension .
Bérard, Jean, Ramirez, Alejandro (2007)
Electronic Communications in Probability [electronic only]
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Bérard, Jean, Ramirez, Alejandro (2007)
Electronic Communications in Probability [electronic only]
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Zachary, Stan, Foss, S.G. (2006)
Sibirskij Matematicheskij Zhurnal
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Duheille-Bienvenüe, Frédérique, Guillotin-Plantard, Nadine (2003)
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Benjamini, Itai, Wilson, David B. (2003)
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Dolgopyat, Dmitry, Liverani, Carlangelo (2009)
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Eckhoff, Maren, Rolles, Silke W.W. (2009)
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I. Kopocińska, B. Kopociński (1987)
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Popov, Serguei, Vachkovskaia, Marina (2005)
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Guillotin-Plantard, Nadine, Le Ny, Arnaud (2008)
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Sznitman, Alain-Sol (2009)
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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...
N. Zygouras (2013)
Annales de l'I.H.P. Probabilités et statistiques
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We consider a random walk in a random potential, which models a situation of a random polymer and we study the annealed and quenched costs to perform long crossings from a point to a hyperplane. These costs are measured by the so called Lyapounov norms. We identify situations where the point-to-hyperplane annealed and quenched Lyapounov norms are different. We also prove that in these cases the polymer path exhibits localization.