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We establish strong mixing for the $\mathbb Z^d$-periodic, infinite horizon,Lorentz gas flow for continuous observables with compact support. The essentialfeature of this natural class of observables is that their support may containpoints with infinite free flights. Dealing with such a class of functions is aserious challenge and there is no analogue of it in the finite horizon case.The mixing result for the aforementioned class of functions is obtained via newresults: 1) mixing for continuous observables with compact support consistingof configurations at a bounded time from the closest collision; 2) atightness-type result that allows us to control the configurations with longfree flights. To prove 1), we establish a mixing local limit theorem for theSinai billiard flow with infinite horizon, previously an open question.

Strong mixing for the periodic Lorentz gas flow with infinite horizon