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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Benjamini, Itai, Izkovsky, Roey, Kesten, Harry (2007)
Electronic Journal of Probability [electronic only]
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Holmes, Mark P. (2009)
Electronic Communications in Probability [electronic only]
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Eckhoff, Maren, Rolles, Silke W.W. (2009)
Electronic Communications in Probability [electronic only]
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Duheille-Bienvenüe, Frédérique, Guillotin-Plantard, Nadine (2003)
Electronic Communications in Probability [electronic only]
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Guillotin-Plantard, Nadine, Le Ny, Arnaud (2008)
Electronic Communications in Probability [electronic only]
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Nadine Guillotin-Plantard, Clémentine Prieur (2010)
ESAIM: Probability and Statistics
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We prove a central limit theorem for linear triangular arrays under weak dependence conditions. Our result is then applied to dependent random variables sampled by a -valued transient random walk. This extends the results obtained by [N. Guillotin-Plantard and D. Schneider, (2003) 477–497]. An application to parametric estimation by random sampling is also provided.
Sznitman, Alain-Sol (2009)
Electronic Journal of Probability [electronic only]
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Benjamini, Itai, Wilson, David B. (2003)
Electronic Communications in Probability [electronic only]
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Philippe Carmona (2010)
ESAIM: Probability and Statistics
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The sequence of random probability measures that gives a path of length , times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the Legendre transform of the free energy of the associated directed polymer in a random environment. Consequences on the asymptotics of the typical number of paths whose collected weight is above a fixed proportion are then drawn.
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...