We prove a quenched functional central limit theorem for a one-dimensional random walk driven by a simple symmetric exclusion process. This model can be viewed as a special case of the random walk in a balanced random environment, for which the weak quenched limit is constructed as a function of the invariant measure of the environment viewed from the walk. We bypass the need to show the existence of this invariant measure. Instead, we find the limit of the quadratic variation of the walk and give an explicit formula for it.
JP was supported in part by a Simons Foundation Collaboration Grant #635064.
We thank the anonymous referee for alerting us to the competing conjectures in  and .
"Variable speed symmetric random walk driven by the simple symmetric exclusion process." Electron. J. Probab. 27 1 - 14, 2022. https://doi.org/10.1214/21-EJP735