Professor Ian Melbourne
Professor of Mathematics
Teaching Responsibilities 2020/21:
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.
Online Workshop. Ergodicity: six different viewpoints. Warwick, 18 May 2020. Organizers: J-P. Bouchaud, R. Farmer, R. MacKay and I. Melbourne.
Workshop. Statistical aspects of geodesic flows in nonpositive curvature. Warwick, 20 to 23 January 2020. Organizers: Y. Lima and I. Melbourne.
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.