Recurrence and transience for long-range reversible random walks on a random point process

Details Recurrence and transience for long-range reversible random walks on a random point process Recurrence and transience for long-range reversible random walks on a random point process

2008-11-27

arxiv.org/abs/0811.4623v1

Mathematics

Probability

34 pages

Scientific paper

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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