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arXiv · 1411.2707

Anomalous threshold behavior of long range random walks

Mathav Murugan·Laurent Saloff-Coste
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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.

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Mathav Murugan, Laurent Saloff-Coste. 2015-09-01. Anomalous threshold behavior of long range random walks. https://doi.org/10.1214/ejp.v20-3989

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