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H 1 ​Levy diffusion of dispersing billiards with flat points

Auteurs : Zhang, Hong-Kun (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : ​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

    Codes MSC :
    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

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 15/11/2018
      Date de captation : 31/10/2018
      Collection : Research talks ; Dynamical Systems and Ordinary Differential Equations ; Probability and Statistics
      Format : MP4
      Durée : 00:52:53
      Domaine : Dynamical Systems & ODE ; Probability & Statistics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2018-10-31_Zhang.mp4

    Informations sur la rencontre

    Nom de la rencontre : Probabilistic limit theorems for dynamical systems / Théorèmes limites probabilistes pour les systèmes dynamiques
    Organisateurs de la rencontre : Melbourne, Ian ; Pène, Françoise ; Volny, Dalibor
    Dates : 29/10/2018 - 02/11/2018
    Année de la rencontre : 2018
    URL Congrès : https://conferences.cirm-math.fr/1997.html

    Citation Data

    DOI : 10.24350/CIRM.V.19471903
    Cite 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


    Voir aussi

    Bibliographie

    1. ​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

    2. Jung, P., & Zhang, H.-K. (2018). Stable laws for chaotic billiards with cusps at flat points. - https://arxiv.org/abs/1611.00879

    3. Jung, P., Pène, F., & Zhang, H.-K. (2018). Convergence to $\alpha$-stable Lévy motion for chaotic billiards with several cusps at flat points. - https://arxiv.org/abs/1809.08021

    4. 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

    5. Mohr, L., & Zhang, H.-K. (2017). Supperdiffusions for certain nonuniformly hyperbolic systems. - https://arxiv.org/abs/1709.00528

    6. Pène, F., & Saussol, B. (2018). Spatio-temporal Poisson processes for visits to small sets. - https://arxiv.org/abs/1803.06865

    7. 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

    8. 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

    9. 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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