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2001 On Recurrent and Transient Sets of Inhomogeneous Symmetric Random Walks
Giambattista Giacomin, Gustavo Posta
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Electron. Commun. Probab. 6(none): 39-53 (2001). DOI: 10.1214/ECP.v6-1033


We consider a continuous time random walk on the $d$-dimensional lattice $\mathbb{Z}^d$: the jump rates are time dependent, but symmetric and strongly elliptic with ellipticity constants independent of time. We investigate the implications  of heat kernel estimates on recurrence-transience  properties of the walk and we give conditions for recurrence as well as for transience: we give applications of these conditions  and discuss them in relation with the (optimal) Wiener test available in the time independent context. Our approach relies on estimates on the time spent by the walk in a set and on a 0-1 law. We show also that, still via heat kernel estimates, one can avoid using a 0-1 law, achieving this way quantitative estimates on more general hitting probabilities.


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Giambattista Giacomin. Gustavo Posta. "On Recurrent and Transient Sets of Inhomogeneous Symmetric Random Walks." Electron. Commun. Probab. 6 39 - 53, 2001.


Accepted: 18 January 2001; Published: 2001
First available in Project Euclid: 19 April 2016

zbMATH: 0976.60073
MathSciNet: MR1831800
Digital Object Identifier: 10.1214/ECP.v6-1033

Primary: 60J25
Secondary: 60J75, 82B41


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