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

Pietro Caputo (Università di Roma Tre)
Alessandra Faggionato (University La Sapienza Rome)
Alexandre Gaudilliere (University of Roma Tre)

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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Pages: 2580-2616

Publication Date: November 3, 2009

DOI: 10.1214/EJP.v14-721

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