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.
"Non-trivial linear bounds for a random walk driven by a simple symmetric exclusion process." Electron. J. Probab. 19 1 - 18, 2014. https://doi.org/10.1214/EJP.v19-3159