Ian Melbourne's Publication List

Publications on Statistical Laws (excluding anomalous diffusion)

1. Y. Lima, C. Matheus and I. Melbourne. Polynomial decay of correlations for nonpositively curved surfaces.
   Trans. Amer. Math. Soc. 377 (2024) 6043-6095. (abstract, pdf file)

2. A. Korepanov, Z. Kosloff and I. Melbourne. Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 1.
   Ann. Inst. H. Poincaré (B) Probab. Statist. 58 (2022) 1305-1327. (abstract, pdf file, published version)

3. M. Galton and I. Melbourne. Iterated invariance principle for slowly mixing dynamical systems.
   Ann. Inst. H. Poincaré (B) Probab. Statist. 58 (2022) 1284-1304. (abstract, pdf file, published version)

4. P. Eslami, I. Melbourne and S. Vaienti. Sharp statistical properties for a family of multidimensional nonMarkovian nonconformal intermittent maps.
   Adv. Math. 388 (2021) 107853. (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. 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)
   

7. V. Araújo and I. Melbourne. Mixing properties and statistical limit theorems for singular hyperbolic flows without a smooth stable foliation.
   Adv. Math. 349 (2019) 212-245. (abstract, pdf file)

8. P. Bálint and I. Melbourne. Statistical properties for flows with unbounded roof function, including the Lorenz attractor.
   J. Stat. Phys. 172 (2018) 1101-1126. (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. G. Gottwald and I. Melbourne. Central limit theorems and suppression of anomalous diffusion for systems with symmetry.
    Nonlinearity 29 (2016) 2941-2960. (abstract, pdf file)

11. 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)

12. V. Araújo, I. Melbourne and P. Varandas. Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps.
    Commun. Math. Phys. 340 (2015) 901-938. (abstract, pdf file)

13. S. Gouëzel and I. Melbourne. Moment bounds and concentration inequalities for slowly mixing dynamical systems.
    Electron.J. Probab. 19 (2014) 1-30. (abstract, or pdf file)

14. S. Luzzatto and I. Melbourne. Statistical properties and decay of correlations for interval maps with critical points and singularities.
    Commun. Math. Phys. 320 (2013) 21-35. (abstract, pdf file)

15. 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)

16. I. Melbourne. Large and moderate deviations for slowly mixing dynamical systems.
    Proc. Amer. Math. Soc. 137 (2009) 1735-1741. (abstract, pdf file)

17. 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)

18. I. Melbourne and M. Nicol. Large deviations for nonuniformly hyperbolic systems.
    Trans. Amer. Math. Soc. 360 (2008) 6661-6676. (abstract, pdf file)

19. M. Holland and I. Melbourne. Central limit theorems and invariance principles for Lorenz attractors.
    J London Math Soc 76 (2007) 345-364. (abstract, pdf file)

20. I. Melbourne and M. Nicol. Almost sure invariance principle for nonuniformly hyperbolic systems.
    Commun. Math. Phys. 260 (2005) 131-146. (abstract, pdf file)

21. M. Field, I. Melbourne, M. Nicol and A. Török. Statistical properties of compact group extensions of hyperbolic flows and their time one maps.
    Disc. Cont. Dyn. Syst. 12 (2005) 79-96. (abstract, pdf file)

22. I. Melbourne and A. Török. Statistical limit theorems for suspension flows.
    Israel Journal of Math. 144 (2004) 191-209. (abstract, pdf file)

23. I. Melbourne and M. Nicol. Statistical properties of endomorphisms and compact group extensions.
    J. London Math. Soc. 70 (2004) 427-446. (abstract, pdf file)

24. I. Melbourne and M. Nicol. Statistical limit laws for equivariant observations.
    Stoch. Dyn. 4 (2004) 1-13. (abstract, pdf file)

25. M. Field, I. Melbourne and A. Török. Decay of correlations, central limit theorems and approximation by Brownian motion for compact Lie group extensions.
    Ergodic Theory Dyn. Syst. 23 (2003) 87-110. (abstract, pdf file)

26. I. Melbourne and A. Török. Central limit theorems and invariance principles for time-one maps of hyperbolic flows.
    Commun. Math. Phys. 229 (2002) 57-71. (abstract, pdf file)

27. P. Ashwin, I. Melbourne and M. Nicol. Hypermeander of spirals; local bifurcations and statistical properties.
    Physica D 156 (2001) 364-382. (abstract, pdf file)