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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

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 times ...

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