## Electronic Communications in Probability

### On Recurrent and Transient Sets of Inhomogeneous Symmetric Random Walks

#### Abstract

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.

#### Article information

Source
Electron. Commun. Probab., Volume 6 (2001), paper no. 4, 39-53.

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

https://projecteuclid.org/euclid.ecp/1461097549

Digital Object Identifier
doi:10.1214/ECP.v6-1033

Mathematical Reviews number (MathSciNet)
MR1831800

Zentralblatt MATH identifier
0976.60073

Rights

#### Citation

Giacomin, Giambattista; Posta, Gustavo. On Recurrent and Transient Sets of Inhomogeneous Symmetric Random Walks. Electron. Commun. Probab. 6 (2001), paper no. 4, 39--53. doi:10.1214/ECP.v6-1033. https://projecteuclid.org/euclid.ecp/1461097549

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