A functional limit theorem for a 2D-random walk with dependent marginals.
Guillotin-Plantard, Nadine, Le Ny, Arnaud (2008)
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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Zachary, Stan, Foss, S.G. (2006)
Sibirskij Matematicheskij Zhurnal
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Duheille-Bienvenüe, Frédérique, Guillotin-Plantard, Nadine (2003)
Electronic Communications in Probability [electronic only]
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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...
Agnieszka Jurlewicz, Mark M. Meerschaert, Hans-Peter Scheffler (2011)
Studia Mathematica
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In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW model is useful in physics, to model diffusing particles. Its scaling limit is a time-changed process, whose densities solve an anomalous diffusion equation. This paper develops limit theory and governing equations for cluster CTRW, in which a random number of jumps cluster together into a single jump. The clustering introduces a dependence between the waiting times and jumps that significantly...
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.
R. Kaufman (1970)
Studia Mathematica
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Agnieszka Jurlewicz
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Kifer, Yuri (1998)
Documenta Mathematica
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Mustafa, Ghulam, Nosh, Nusrat Anjum, Rashid, Abdur (2005)
Lobachevskii Journal of Mathematics
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G. Trybuś (1974)
Applicationes Mathematicae
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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...
Nguyen, Quy Hy, Nguyen, Ngoc Cuong (2015-12-08T12:59:38Z)
Acta Universitatis Lodziensis. Folia Mathematica
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S. K. Srinivasan, K. S. S. Iyer (1965)
Applicationes Mathematicae
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Bérard, Jean, Ramirez, Alejandro (2007)
Electronic Communications in Probability [electronic only]
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