On constrained annealed bounds for pinning and wetting models.
Caravenna, Francesco, Giacomin, Giambattista (2005)
Electronic Communications in Probability [electronic only]
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Caravenna, Francesco, Giacomin, Giambattista (2005)
Electronic Communications in Probability [electronic only]
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Toninelli, Fabio Lucio (2009)
Electronic Journal of Probability [electronic only]
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N. Berger, M. Biskup, C. E. Hoffman, G. Kozma (2008)
Annales de l'I.H.P. Probabilités et statistiques
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We consider the nearest-neighbor simple random walk on ℤ, ≥2, driven by a field of bounded random conductances ∈[0, 1]. The conductance law is i.i.d. subject to the condition that the probability of >0 exceeds the threshold for bond percolation on ℤ. For environments in which the origin is connected to infinity by bonds with positive conductances, we study the decay of the 2-step return probability . We prove that is bounded by a random constant...
Velenik, Yvan (2006)
Probability Surveys [electronic only]
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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 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.
Matthias Birkner, Rongfeng Sun (2010)
Annales de l'I.H.P. Probabilités et statistiques
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We study a random walk pinning model, where conditioned on a simple random walk on ℤ acting as a random medium, the path measure of a second independent simple random walk up to time is Gibbs transformed with hamiltonian − (, ), where (, ) is the collision local time between and up to time . This model arises naturally in various contexts, including the study of the parabolic Anderson model with moving catalysts, the parabolic Anderson model with brownian...
Külske, Christof, Orlandi, Enza (2006)
Electronic Communications in Probability [electronic only]
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Julie Scholler (2014)
ESAIM: Probability and Statistics
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We pursue the study of a random coloring first passage percolation model introduced by Fontes and Newman. We prove that the asymptotic shape of this first passage percolation model continuously depends on the law of the coloring. The proof uses several couplings, particularly with greedy lattice animals.
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...