Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 21 (2016), paper no. 15, 11 pp.
Zero-one law for directional transience of one-dimensional random walks in dynamic random environments
We prove the trichotomy between transience to the right, transience to the left and recurrence of one-dimensional nearest-neighbour random walks in dynamic random environments under fairly general assumptions, namely: stationarity under space-time translations, ergodicity under spatial translations, and a mild ellipticity condition. In particular, the result applies to general uniformly elliptic models and also to a large class of non-uniformly elliptic cases that are i.i.d. in space and Markovian in time. An immediate consequence is the recurrence of models that are symmetric with respect to reflection through the origin.
Electron. Commun. Probab., Volume 21 (2016), paper no. 15, 11 pp.
Received: 13 July 2015
Accepted: 26 January 2016
First available in Project Euclid: 19 February 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F20: Zero-one laws 60K37: Processes in random environments
Secondary: 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41] 82C44: Dynamics of disordered systems (random Ising systems, etc.)
Orenshtein, Tal; Soares dos Santos, Renato. Zero-one law for directional transience of one-dimensional random walks in dynamic random environments. Electron. Commun. Probab. 21 (2016), paper no. 15, 11 pp. doi:10.1214/16-ECP4426. https://projecteuclid.org/euclid.ecp/1455897057