The Annals of Probability
- Ann. Probab.
- Volume 47, Number 5 (2019), 3003-3054.
On the transient (T) condition for random walk in mixing environment
We prove a ballistic strong law of large numbers and an invariance principle for random walks in strong mixing environments, under condition $(T)$ of Sznitman (cf. Ann. Probab. 29 (2001) 724–765). This weakens for the first time Kalikow’s ballisticity assumption on mixing environments and proves the existence of arbitrary finite order moments for the approximate regeneration time of F. Comets and O. Zeitouni (Israel J. Math. 148 (2005) 87–113). The main technical tool in the proof is the introduction of renormalization schemes, which had only been considered for i.i.d. environments.
Ann. Probab., Volume 47, Number 5 (2019), 3003-3054.
Received: February 2018
Revised: November 2018
First available in Project Euclid: 22 October 2019
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Guerra Aguilar, Enrique. On the transient (T) condition for random walk in mixing environment. Ann. Probab. 47 (2019), no. 5, 3003--3054. doi:10.1214/18-AOP1330. https://projecteuclid.org/euclid.aop/1571731443