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2019 New examples of ballistic RWRE in the low disorder regime
Alejandro F. Ramírez, Santiago Saglietti
Electron. J. Probab. 24: 1-20 (2019). DOI: 10.1214/19-EJP374


We give a new criterion for ballistic behavior of random walks in random environments which are low disorder perturbations of the simple symmetric random walk on $\mathbb{Z} ^{d}$, for $d\geq 2$. This extends the results from 2003 established by Sznitman in [12] and, in particular, allow us to give new examples of ballistic RWREs in dimension $d=3$ which do not satisfy Kalikow’s condition, through a new sharp version of Kalikow’s criteria. Essentially, this new criterion states that ballisticity occurs whenever the average local drift of the walk is not too small when compared to the standard deviation of the environment. Its proof relies on applying coarse-graining methods together with a variation of the Azuma-Hoeffding concentration inequality in order to verify the fulfillment of a ballisticity condition by Berger, Drewitz and Ramírez.


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Alejandro F. Ramírez. Santiago Saglietti. "New examples of ballistic RWRE in the low disorder regime." Electron. J. Probab. 24 1 - 20, 2019.


Received: 28 April 2019; Accepted: 16 October 2019; Published: 2019
First available in Project Euclid: 9 November 2019

zbMATH: 07142921
MathSciNet: MR4029430
Digital Object Identifier: 10.1214/19-EJP374

Primary: 60K37, 82C41, 82D30


Vol.24 • 2019
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