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2009 Recurrence and Transience for Long-Range Reversible Random Walks on a Random Point Process
Pietro Caputo, Alessandra Faggionato, Alexandre Gaudilliere
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Electron. J. Probab. 14: 2580-2616 (2009). DOI: 10.1214/EJP.v14-721

Abstract

We consider reversible random walks in random environment obtained from symmetric long-range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and the jump rate function. For recurrent models we obtain almost sure estimates on effective resistances in finite boxes. For transient models we construct explicit fluxes with finite energy on the associated electrical network.

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Pietro Caputo. Alessandra Faggionato. Alexandre Gaudilliere. "Recurrence and Transience for Long-Range Reversible Random Walks on a Random Point Process." Electron. J. Probab. 14 2580 - 2616, 2009. https://doi.org/10.1214/EJP.v14-721

Information

Accepted: 3 November 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1191.60120
MathSciNet: MR2570012
Digital Object Identifier: 10.1214/EJP.v14-721

Subjects:
Primary: 60K37
Secondary: 60G55, 60J45

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