Regular and Stochastic Behaviour in Dynamical Systems

Mixing estimate for the periodic Lorentz gas flow in infinite horizon

speaker: Francoise Pène (Université de Brest)

abstract: Motivated by the study of the mixing rate for natural observables of the Z^d-periodic Lorentz gas flow in infinite horizon, we have to face different difficulties due to the non-integrability of free flight. We establish a first mixing estimate for some observables (that are natural for the suspension flow representation but not for the original flow) thanks to limit theorems for the Sinai billiard map: namely the MLLT (Mixing Local Limit Theorem) coming from Szász and Varjú's LLT, combined with a sharp Local Large Deviation (LLD). To go from this first mixing estimate to the mixing estimate for natural observables (the support of which may contain configurations with infinite free flight), we establish a tightness-type result, the proof of which uses and combines subtly a series of additional intermediate results such as a MLLT with very good error terms, a Large Deviation estimate for the number of collisions, etc. This work is in collaboration with Dalia Terhesiu. The LLD was proved in collaboration with Ian Melbourne and Dalia Terhesiu.

timetable:
Tue 6 Jun, 9:00 - 10:00, Aula Dini
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