Displaying similar documents to “A note on percolation on ℤ d : isoperimetric profile via exponential cluster repulsion.”

Anomalous heat-kernel decay for random walk among bounded random conductances

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 𝖯 ω 2 n ( 0 , 0 ) . We prove that 𝖯 ω 2 n ( 0 , 0 ) is bounded by a random constant...

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...