## Electronic Journal of Probability

### 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.

#### Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 74, 21 pp.

Dates
Accepted: 28 June 2015
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465067180

Digital Object Identifier
doi:10.1214/EJP.v20-3989

Mathematical Reviews number (MathSciNet)
MR3371433

Zentralblatt MATH identifier
1321.60090

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60J75: Jump processes 60J15

Rights

#### Citation

Murugan, Mathav; Saloff-Coste, Laurent. Anomalous threshold behavior of long range random walks. Electron. J. Probab. 20 (2015), paper no. 74, 21 pp. doi:10.1214/EJP.v20-3989. https://projecteuclid.org/euclid.ejp/1465067180

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