Electronic Journal of Probability

Recurrence and Transience for Long-Range Reversible Random Walks on a Random Point Process

Pietro Caputo, Alessandra Faggionato, and Alexandre Gaudilliere

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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.

Article information

Source
Electron. J. Probab., Volume 14 (2009), paper no. 90, 2580-2616.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819551

Digital Object Identifier
doi:10.1214/EJP.v14-721

Mathematical Reviews number (MathSciNet)
MR2570012

Zentralblatt MATH identifier
1191.60120

Subjects
Primary: 60K37: Processes in random environments
Secondary: 60G55: Point processes 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]

Keywords
random walk in random environment recurrence transience point process electrical network

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Caputo, Pietro; Faggionato, Alessandra; Gaudilliere, Alexandre. Recurrence and Transience for Long-Range Reversible Random Walks on a Random Point Process. Electron. J. Probab. 14 (2009), paper no. 90, 2580--2616. doi:10.1214/EJP.v14-721. https://projecteuclid.org/euclid.ejp/1464819551


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