Anomalous threshold behavior of long range random walks
Probability
2015-09-03 v2
Abstract
We consider weighted graphs satisfying sub-Gaussian estimate for the natural random walk. On such graphs, we study symmetric Markov chains with heavy tailed jumps. We establish a threshold behavior of such Markov chains when the index governing the tail heaviness (or jump index) equals the escape time exponent (or walk dimension) of the sub-Gaussian estimate. In a certain sense, this generalizes the classical threshold corresponding to the second moment condition.
Cite
@article{arxiv.1411.2707,
title = {Anomalous threshold behavior of long range random walks},
author = {Mathav Murugan and Laurent Saloff-Coste},
journal= {arXiv preprint arXiv:1411.2707},
year = {2015}
}
Comments
24 pages; incorporated referee comments; published in the Electronic Journal of Probability (http://ejp.ejpecp.org/article/view/3989)