Displaying similar documents to “Approximation of Lévy-Feller diffusion by random walk.”

Cluster continuous time random walks

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...

Scaling of a random walk on a supercritical contact process

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...

Superdiffusivity for directed polymer in corelated random environment

Hubert Lacoin (2010)

Actes des rencontres du CIRM

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The directed polymer in random environment models the behavior of a polymer chain in a solution with impurities. It is a particular case of random walk in random environment. In 1 + 1 dimensional environment is has been shown by Petermann that this random walk is superdiffusive. We show superdiffusivity properties are reinforced were there are long ranged correlation in the environment and that super diffusivity also occurs in higher dimensions.

Strong disorder in semidirected random polymers

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.

Perturbing transient random walk in a random environment with cookies of maximal strength

Elisabeth Bauernschubert (2013)

Annales de l'I.H.P. Probabilités et statistiques

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We consider a left-transient random walk in a random environment on ℤ that will be disturbed by cookies inducing a drift to the right of strength 1. The number of cookies per site is i.i.d. and independent of the environment. Criteria for recurrence and transience of the random walk are obtained. For this purpose we use subcritical branching processes in random environments with immigration and formulate criteria for recurrence and transience for these processes.

Random walk in random environment with asymptotically zero perturbation

M.V. Menshikov, Andrew R. Wade (2006)

Journal of the European Mathematical Society

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We give criteria for ergodicity, transience and null-recurrence for the random walk in random environment on ℤ + = { 0 , 1 , 2 , ⋯ } , with reflection at the origin, where the random environment is subject to a vanishing perturbation. Our results complement existing criteria for random walks in random environments and for Markov chains with asymptotically zero drift, and are significantly different from the previously studied cases. Our method is based on a martingale technique—the method of Lyapunov functions. ...

Homogenization results for a linear dynamics in random Glauber type environment

Cédric Bernardin (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We consider an energy conserving linear dynamics that we perturb by a Glauber dynamics with random site dependent intensity. We prove hydrodynamic limits for this non-reversible system in random media. The diffusion coefficient turns out to depend on the random field only by its statistics. The diffusion coefficient defined through the Green–Kubo formula is also studied and its convergence to some homogenized diffusion coefficient is proved.