We study models of continuous-time, symmetric random walks in random environment on the d-dimensional integer lattice, driven by a field of i.i.d random nearest-neighbor conductances bounded only from above with a power law tail near 0. We are interested in estimating the quenched asymptotic behavior of the on-diagonal heat-kernel. We show that the spectral dimension is standard when we lighten sufficiently the tails of the conductances. As an expected consequence, the same result holds for the discrete-time case.
"Standard Spectral Dimension for the Polynomial Lower Tail Random Conductances Model." Electron. J. Probab. 15 2069 - 2086, 2010. https://doi.org/10.1214/EJP.v15-839