Functional CLT for random walk among bounded random conductances.

Biskup, Marek; Prescott, Timothy M.

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

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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...

The scaling limit of senile reinforced random walk.

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The quenched invariance principle for random walks in random environments admitting a bounded cycle representation

Jean-Dominique Deuschel, Holger Kösters (2008)

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

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We derive a quenched invariance principle for random walks in random environments whose transition probabilities are defined in terms of weighted cycles of bounded length. To this end, we adapt the proof for random walks among random conductances by Sidoravicius and Sznitman ( (2004) 219–244) to the non-reversible setting.