Abstract
Linear bounds are obtained for the displacement of a random walk in a dynamic random environment given by a one-dimensional simple symmetric exclusion process in equilibrium. The proof uses an adaptation of multiscale renormalization methods of Kesten and Sidoravicius.
Highlights
Linear bounds are obtained for the displacement of a random walk in a dynamic random environment given by a one-dimensional simple symmetric exclusion process in equilibrium
We discuss linear scaling properties of a random walk in a dynamic random environment (RWDRE), where the role of the random environment is taken by a one-dimensional simple symmetric exclusion process (SSEP)
While many results for RWDRE have been obtained in the past few years for random environments exhibiting uniform and fast enough mixing, very little is known when the random environment mixes in a non-uniform way, as happens in the SSEP
Summary
It is easy to see, with a coupling argument, that W lies between two homogeneous random walks with drifts v0 and v1. Any subsequential limit of t−1Wt as t → ∞ lies in the interval [v0, v1] Would it be possible, even along a subsequence, for W to travel at one of the extremal speeds? The proof of Theorem 1.1 given here is based on the multiscale analysis scheme put forth by Kesten in Sidoravicius [11], and seems exceedingly heavy for such a simple fact. It has the advantage of being easier to EJP 19 (2014), paper 49. The analogous result for the supercritical contact process can be reobtained with this approach
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
