Zero-one law for directional transience of one-dimensional random walks in dynamic random environments
- Orenshtein, Tal
- Soares dos Santos, Renato
2010 Mathematics Subject Classification
- 60F20 60K37 82B41 82C44
- random walk, dynamic random environment, zero-one law, directional transience, recurrence
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.
- Electron. Comm. Probab., 21 (2016), pp. 15/1--15/11.