Anomalous threshold behavior of long range random walks

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.

24 pages; incorporated referee comments; published in the Electronic Journal of Probability (http://ejp.ejpecp.org/article/view/3989)

References in corpus (2)

• Transition probability estimates for long range random walks
• Random walks driven by low moment measures

Cited by in corpus (3)

• Transition probability estimates for long range random walks
• Subordinated Markov processes: sharp estimates for heat kernels and Green functions
• Stability results for symmetric jump processes on metric measure spaces with atoms. Long version