Aperiodic and linearly repetitive Lorentz gases of finite horizon are not exponentially mixing

Abstract

We prove that aperiodic and linearly repetitive Lorentz gases with finite horizon are not mixing with exponential or stretched exponential speed in any dimension for any class of Hölder observables. We also bound the polynomial speed of mixing for observables in the Hölder space $H_{\alpha }$ depending on $\alpha$.