Electronic Communications in Probability

Monotone interaction of walk and graph: recurrence versus transience

Amir Dembo, Ruojun Huang, and Vladas Sidoravicius

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We consider recurrence versus transience for models of random walks on growing in time, connected subsets $\mathbb{G}_t$ of some fixed locally finite, connected graph, in which monotone interaction enforces such growth as a result of visits by the walk (or probes it sent), to the neighborhood of the boundary of $\mathbb{G}_t$.

Article information

Electron. Commun. Probab., Volume 19 (2014), paper no. 76, 12 pp.

Accepted: 6 November 2014
First available in Project Euclid: 7 June 2016

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50] 60G50: Sums of independent random variables; random walks

Recurrence interacting particle system reinforced random walk random walk on growing domains

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Dembo, Amir; Huang, Ruojun; Sidoravicius, Vladas. Monotone interaction of walk and graph: recurrence versus transience. Electron. Commun. Probab. 19 (2014), paper no. 76, 12 pp. doi:10.1214/ECP.v19-3607. https://projecteuclid.org/euclid.ecp/1465316778

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