Ian Melbourne's Publication List

Publications on dispersing billiards and Lorentz gases

  1. A. C. Freitas, J. Freitas, I. Melbourne and M. Todd. Convergence to decorated Lévy processes in non-Skorohod topologies for dynamical systems.
    Electron. J. Probab. 29 paper no. 170 (2024) 1-24. (abstract, pdf file)

  2. I. Melbourne, F. Pène and D. Terhesiu. Local large deviations for periodic infinite horizon Lorentz gases.
    J. d'Analyse Math. 152 (2024) 283-316. (abstract, pdf file, link to journal version)

  3. P. Jung, I. Melbourne, F. Pène, P. Varandas and H.-K. Zhang. Necessary and sufficient condition for M2-convergence to a Lévy process for billiards with cusps at flat points.
    Stoch. Dyn. 21 (2021) 2150024, 8 pages. (abstract, pdf file)

  4. H. Bruin, I. Melbourne and D. Terhesiu. Sharp polynomial bounds on decay of correlations for multidimensional nonuniformly hyperbolic systems and billiards.
    Annales Henri Lebesgue 4 (2021) 407-451. (abstract, pdf file)

  5. M. Demers, I. Melbourne and M. Nicol. Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas.
    Nonlinearity 33 (2020) 4095-4113. (abstract, pdf file)

  6. I. Melbourne and P. Varandas. Convergence to a Lévy process in the Skorohod M1 and M2 topologies for nonuniformly hyperbolic systems, including billiards with cusps.
    Commun. Math. Phys. 375 (2020) 653-678. (abstract, pdf file, View only of published version)

  7. M. Antoniou and I. Melbourne. Rate of convergence in the weak invariance principle for deterministic systems.
    Commun. Math. Phys. 369 (2019) 1147-1165. (abstract, pdf file, View only of published version)

  8. P. Bálint, O. Butterley and I. Melbourne. Polynomial decay of correlations for flows, including Lorentz gas examples.
    Commun. Math. Phys. 368 (2019) 55-111. (abstract, pdf file, View only of published version)

  9. A. Korepanov, Z. Kosloff and I. Melbourne. Martingale-coboundary decomposition for families of dynamical systems.
    Annales de l'Institut Henri Poincaré / Analyse Non Lineaire 35 (2018) 859-885. (abstract, pdf file)

  10. I. Melbourne and P. Varandas. A note on statistical properties for nonuniformly hyperbolic systems with slow contraction and expansion.
    Stoch. Dyn. 16 (2016) 1660012 (13 pages) (abstract, pdf file)

  11. I. Melbourne and A. Török. Convergence of moments for Axiom A and nonuniformly hyperbolic flows.
    Ergodic Theory Dyn. Syst. 32 (2012) 1091-1100 (abstract, pdf file)

  12. P. Bálint and I. Melbourne. Decay of correlations and invariance principles for dispersing billiards with cusps, and related planar billiard flows.
    J. Stat. Phys. 133 (2008) 435-447. (abstract, pdf file)

  13. I. Melbourne. Rapid decay of correlations for nonuniformly hyperbolic flows.
    Trans. Amer. Math. Soc. 359 (2007) 2421-2441. (abstract, pdf file)