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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

random walk in random environment recurrence transience point process electrical network

This work is licensed under aCreative Commons Attribution 3.0 License.


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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