| 概要 | I will describe recent progress in the understanding of anomalous (subdiffusive) behavior of the return probabilities for the random walk among i.i.d. random conductances that are bounded but have heavy tails at zero. The occurrence of subdiffusive decay is quite surprising given the fact that the path distribution of the walk obeys a non-degenerate functional CLT in all cases of interest. The subdiffusive behavior arises from trapping: Instead of finding the starting point randomly (the diffusive strategy) the walk might prefer to hide in a nearby trap for a majority of its time and thus ease its passage back (the trapping strategy) Recently, it was understood that the two stated strategies are dominant among all others. Based on a joint paper with N. Berger, C. Hoffman, G. Kozma and recent preprints with O. Boukhadra and with O. Louidor, A. Rozinov and A. Vandenberg-Rodes. |