Levy diffusion of dispersing billiards with flat points | Vidéo | Carmin.tv

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Levy diffusion of dispersing billiards with flat points

By Hong-Kun Zhang

Appears in collection : Probabilistic limit theorems for dynamical systems / Théorèmes limites probabilistes pour les systèmes dynamiques

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.

Information about the video

Date of recording 31/10/2018
Date of publication 15/11/2018
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19471903
Cite this video Zhang, Hong-Kun (31/10/2018). Levy diffusion of dispersing billiards with flat points. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19471903
URL https://dx.doi.org/10.24350/CIRM.V.19471903

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Bibliography

Chernov, N., & Zhang, H.-K. (2005). A family of chaotic billiards with variable mixing rates. Stochastics and Dynamics, 5(4), 535-553 - https://doi.org/10.1142/S0219493705001572
Jung, P., & Zhang, H.-K. (2018). Stable laws for chaotic billiards with cusps at flat points. <arXiv:1611.00879> - https://arxiv.org/abs/1611.00879
Jung, P., Pène, F., & Zhang, H.-K. (2018). Convergence to $\alpha$-stable Lévy motion for chaotic billiards with several cusps at flat points. <arXiv:1809.08021> - https://arxiv.org/abs/1809.08021
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. <arXiv:1709.00528> - https://arxiv.org/abs/1709.00528
Pène, F., & Saussol, B. (2018). Spatio-temporal Poisson processes for visits to small sets. <arXiv:1803.06865> - https://arxiv.org/abs/1803.06865
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

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