Monotone interaction of walk and graph: recurrence versus transience. (English) Zbl 1307.60140

Dembo, Amir; Huang, Ruojun; Sidoravicius, Vladas

Electron. Commun. Probab. 19, Paper No. 76, 12 p. (2014).

Summary: We consider recurrence versus transience for models of random walks on connected subsets \(\mathbb{G}_t\), which are growing in time, of some fixed locally finite 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 \(\mathbb{G}_t\).

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
60G50	Sums of independent random variables; random walks
82C41	Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics

Keywords:

interacting particle system; reinforced random walk; growing domains; recurrence; transience