Professor Ian Melbourne
Professor of Mathematics
Teaching Responsibilities 2023/24:
Term 1: MA433 Fourier Analysis
Term 2: MA254 Theory of ODEs
Research Interests: Ergodic theory and dynamical systems. Links with stochastic analysis.
Workshop: Limit theorems for slowly mixing systems. ICMS, Edinburgh, 6 to 10 June 2022. Organizers: I. Melbourne, F. Pène and M. Todd.
Workshop: The Lorentz gas. Lorentz Center, Leiden, 19 to 23 December 2022. Organizers: L. Avena, F. den Hollander, I. Melbourne, and D. Terhesiu.
Editorial board: Ergodic Theory and Dynamical Systems.
Editorial board: Probability Theory and Related Fields.
Selected recent publications:
D. Kelly and I. Melbourne. Smooth approximation of stochastic differential equations. Annals of Probability 44 (2016) 479-520.
G. A. Gottwald and I. Melbourne. A Huygens principle for diffusion and anomalous diffusion in spatially extended systems. Proc. Natl. Acad. Sci. USA 110 (2013) 8411-8416.
I. Melbourne and D. Terhesiu. Operator renewal theory and mixing rates for dynamical systems with infinite measure. Inventiones Mathematicae 189 (2012) 61-110.
I. Melbourne and M. Nicol. A vector-valued almost sure invariance principle for hyperbolic dynamical systems. Annals of Probability 37 (2009) 478-505.
I. Melbourne. Decay of correlations for slowly mixing flows. Proc. London Math. Soc. 98 (2009) 163-190.
M. Field, I. Melbourne and A. Török. Stability of mixing and rapid mixing for hyperbolic flows. Annals of Math. 166 (2007) 269-291.