Dynamics Seminar

Event Information Mixing estimates for periodic Lorentz gases with finite or infinite horizon
14:10 on Wednesday February 26, 2020
15:00 on Wednesday February 26, 2020
BA6180, Bahen Center, 40 St. George St.
Françoise Pène

Université de Bretagne Occidentale

Periodic Lorentz gases are particular cases of a general framework of Z^d-cover of hyperbolic dynamical system. In this context, the rate of mixing is directly related to the local limit theorem of the step function. This enables us, when the horizon is finite, to obtain an mixing expansion of every order for the collision map, but also for the flow. Contrarily to previous expansions obtained in other contexts of dynamical systems preserving an infinite measure, the coefficients appearing in our expansion are linearly independent. This provides in particular mixing rate for null integral observables. The result for the flow (in the finite horizon case) is a recent joint work with Dmitry Dolgopyat and Péter Nándori. In the more complicated case of infinite horizon, error terms in mixing estimates for the collision map, including results for some null integral observables, have been obtained very recently in a joint work with Dalia Terhesiu.