Professor Ian Melbourne Professor of Mathematics Office: B2.06 Phone: +44 (0)2476 523707 (but use email if you want me to get your message) Email: I dot Melbourne at warwick dot ac dot uk

Teaching Responsibilities 2024/25:

Term 1: MA433 Fourier Analysis

Term 2: MA254 Theory of ODEs

Research Interests: Ergodic theory and dynamical systems. Links with stochastic analysis.

Workshop: One day ergodic theory meeting. Warwick, Wednesday 23 October 2024.

Editorial board: Ergodic Theory and Dynamical Systems.

Editorial board: Probability Theory and Related Fields.

Full list of publications (with downloadable links)

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.