Functional limit theorems for billiards with cusps
speaker: Francoise Pène (Université de Brest)abstract: We are interested in the study of the stochastic properties of billiards in domains with convex scatterers and cusps. For cusps with ordinary contact, a rate of decay of correlations has been established by Chernov and Zhang and a functional limit theorem with a non standard normalization has been proved by Bálint, Chernov and Dolgopyat. For billiards with cusps of higher flatness, Zhang established a rate of decay of correlations depending on the flatness of the cusps. In the case of a single symmetric cusp of higher flatness, Jung and Zhang proved a non standard limit theorem (convergence to a stable random variable). We extend this result by proving a non standard functional limit theorem (convergence to a Lévy process) for more general billiards with cusps (allowing several cusps, with more general shape, possibly assymetric, with possibly different flatness). This is a joint work with Paul Jung and Hong-Kun Zhang
timetable:
Fri 7 Jun, 9:00 - 9:45, Aula Dini
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