Standard Spectral Dimension for the Polynomial Lower Tail Random Conductances model

Details Standard Spectral Dimension for the Polynomial Lower Tail Random Conductances model Standard Spectral Dimension for the Polynomial Lower Tail Random Conductances model

2009-07-26

arxiv.org/abs/0907.4525v3

Mathematics

Probability

Title changed, typos corrected

Scientific paper

We study models of continuous-time, symmetric, $\Z^{d}$-valued random walks in random environments, driven by a field of i.i.d. random nearest-neighbor conductances $\omega_{xy}\in[0,1]$ with a power law with an exponent $\gamma$ near 0. We are interested in estimating the quenched decay of the return probability $P_\omega^{t}(0,0)$, as $t$ tends to $+\infty$. We show that for $\gamma> \frac{d}{2}$, the standard bound turns out to be of the correct logarithmic order. As an expected concequence, the same result holds for the discrete-time case.

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