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Levy diffusion of dispersing billiards with flat points
Multi angle
Authors : Zhang, Hong-Kun (Author of the conference)
CIRM (Publisher )
37A25 - Ergodicity, mixing, rates of mixing
37D25 - Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37D50 - Hyperbolic systems with singularities (billiards, etc.)
60F05 - Central limit and other weak theorems
CIRM (Publisher )
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Abstract :
We investigate the diffusion and statistical properties of Lorentz gas with cusps at flat points. This is a modification of dispersing billiards with cusps. The decay rates are proven to depend on the degree of the flat points, which varies from $n^{-a}$, for $ a\in (0,\infty)$. The stochastic processes driven by these systems enjoy stable law and have super-diffusion driven by Lévy process. This is a joint work with Paul Jung and Françoise Pène.
Keywords : chaotic billiards; Lorentz gas; dispersing billiards; rates of mixing; flat points; Lévy process; Skorohod topology
MSC Codes : Keywords : chaotic billiards; Lorentz gas; dispersing billiards; rates of mixing; flat points; Lévy process; Skorohod topology
37A25 - Ergodicity, mixing, rates of mixing
37D25 - Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37D50 - Hyperbolic systems with singularities (billiards, etc.)
60F05 - Central limit and other weak theorems
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 15/11/2018 Conference Date : 31/10/2018 Subseries : Research talks arXiv category : Dynamical Systems ; Probability Mathematical Area(s) : Dynamical Systems & ODE ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:52:53 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2018-10-31_Zhang.mp4 
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Information on the Event
Event Title : Probabilistic limit theorems for dynamical systems / Théorèmes limites probabilistes pour les systèmes dynamiquesEvent Organizers : Melbourne, Ian ; Pène, Françoise ; Volny, Dalibor Dates : 29/10/2018 - 02/11/2018 Event Year : 2018 Event URL : https://conferences.cirm-math.fr/1997.html
Citation Data
DOI : 10.24350/CIRM.V.19471903Cite this video as: Zhang, Hong-Kun (2018). Levy diffusion of dispersing billiards with flat points. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19471903 URI : http://dx.doi.org/10.24350/CIRM.V.19471903 |
See Also
- [Multi angle] Mixing and the local central limit theorem for hyperbolic dynamical systems / Author of the conference Nándori, Péter.
- [Multi angle] Diffusion limit for a slow-fast standard map / Author of the conference De Simoi, Jacopo.
- [Multi angle] Limit theorems for almost Anosov flows / Author of the conference Terhesiu, Dalia.
- [Post-edited] Growth of normalizing sequences in limit theorems / Author of the conference Gouëzel, Sébastien.
Bibliography
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- Jung, P., & Zhang, H.-K. (2018). Stable laws for chaotic billiards with cusps at flat points.
- Jung, P., Pène, F., & Zhang, H.-K. (2018). Convergence to $\alpha$-stable Lévy motion for chaotic billiards with several cusps at flat points.
- Melbourne, I., & Zweimüller, R. (2015). Weak convergence to stable Lévy processes for nonuniformly hyperbolic dynamical systems. Annales de l'Institut Henri Poincaré. Probabilités et Statistiques, 51(2), 545-556 - https://doi.org/10.1214/13-AIHP586
- Mohr, L., & Zhang, H.-K. (2017). Supperdiffusions for certain nonuniformly hyperbolic systems.
- Pène, F., & Saussol, B. (2018). Spatio-temporal Poisson processes for visits to small sets.
- Tyran-Kamińska, M. (2010). Weak convergence to Lévy stable processes in dynamical systems. Stochastics and Dynamics, 10(2), 263-289 - https://doi.org/10.1142/S0219493710002942
- Zhang, H.-K. (2017). Decay of correlations for billiards with flat points I: channel effects. In A.M. Blokh, L.A. Bunimovich, P.H. Jung, L.G. Oversteegen, & Y.G. Sina (Eds.), Dynamical Systems, Ergodic Theory, and Probability (pp. 239-286). Providence, RI: American Mathematical Society - https://doi.org/10.1090/conm/698/13983
- Zhang, H.-K. (2017). Decay of correlations for billiards with flat points II: cusps effect. In A.M. Blokh, L.A. Bunimovich, P.H. Jung, L.G. Oversteegen, & Y.G. Sina (Eds.), Dynamical Systems, Ergodic Theory, and Probability (pp. 287-316). Providence, RI: American Mathematical Society - https://doi.org/10.1090/conm/698/13983
