Daniel Kious

Sharp threshold for the ballisticity of the random walk on the exclusion process

We study a non-reversible random walk advected by the symmetric simple exclusion process, so that the walk has a local drift of opposite sign when sitting atop an occupied or an empty site. We prove that the back-tracking probability of the walk exhibits a sharp transition as the...

Fluctuation bounds for symmetric random walks on dynamic environments via Russo–Seymour–Welsh

In this article we prove a lower bound for the fluctuations of symmetric random walks on dynamic random environments in dimension 1+1 in the perturbative regime where the walker is weakly influenced by the environment. We suppose that the random environment is invariant with resp...