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.
Citation
Mathav Murugan. Laurent Saloff-Coste. "Anomalous threshold behavior of long range random walks." Electron. J. Probab. 20 1 - 21, 2015. https://doi.org/10.1214/EJP.v20-3989
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