Displaying similar documents to “Random Walks and Random Environments, Volume 1 : Random Walks - Barry D. Hughes.”

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.

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 + = { 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. ...