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Recurrence and transience for long-range reversible random walks on a random point process. (English) Zbl 1191.60120
Summary: 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.

MSC:
60K37 Processes in random environments
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60J45 Probabilistic potential theory
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