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Displaying similar documents to “Anomalous heat-kernel decay for random walk among bounded random conductances”

Connectivity bounds for the vacant set of random interlacements

Vladas Sidoravicius, Alain-Sol Sznitman (2010)

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

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The model of random interlacements on ℤ, ≥3, was recently introduced in [Vacant set of random interlacements and percolation. Available at http://www.math.ethz.ch/u/sznitman/preprints]. A non-negative parameter parametrizes the density of random interlacements on ℤ. In the present note we investigate connectivity properties of the vacant set left by random interlacements at level , in the non-percolative regime >∗, with ∗ the non-degenerate critical parameter for the percolation...

Giant vacant component left by a random walk in a random d-regular graph

Jiří Černý, Augusto Teixeira, David Windisch (2011)

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

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We study the trajectory of a simple random walk on a -regular graph with ≥ 3 and locally tree-like structure as the number of vertices grows. Examples of such graphs include random -regular graphs and large girth expanders. For these graphs, we investigate percolative properties of the set of vertices not visited by the walk until time , where > 0 is a fixed positive parameter. We show that this so-called set exhibits a phase transition in in the following sense: there exists...

Scaling limit of the random walk among random traps on ℤd

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...

Averaged large deviations for random walk in a random environment

Atilla Yilmaz (2010)

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

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In his 2003 paper, Varadhan proves the averaged large deviation principle for the mean velocity of a particle taking a nearest-neighbor random walk in a uniformly elliptic i.i.d. environment on ℤ with ≥1, and gives a variational formula for the corresponding rate function . Under Sznitman’s transience condition (), we show that is strictly convex and analytic on a non-empty open set , and that the true velocity of the particle is an element (resp. in...

Limit theorem for random walk in weakly dependent random scenery

Nadine Guillotin-Plantard, Clémentine Prieur (2010)

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

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Let =( )≥0 be a random walk on ℤ and =( )∈ℤ a stationary random sequence of centered random variables, independent of . We consider a random walk in random scenery that is the sequence of random variables ( )≥0, where =∑=0 , ∈ℕ. Under a weak dependence assumption on the scenery we prove a functional limit theorem generalizing Kesten and Spitzer’s [ (1979) 5–25]...

Discrete random processes with memory: Models and applications

Tomáš Kouřim, Petr Volf (2020)

Applications of Mathematics

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The contribution focuses on Bernoulli-like random walks, where the past events significantly affect the walk's future development. The main concern of the paper is therefore the formulation of models describing the dependence of transition probabilities on the process history. Such an impact can be incorporated explicitly and transition probabilities modulated using a few parameters reflecting the current state of the walk as well as the information about the past path. The behavior...