报告题目：Convergence to Levy processes for nonuniformly hyperbolic dynamical systems

报 告 人：Ian Melbourne 教授（英国华威大学）

报告时间：2026年7月23日（星期四） 15:30-16:30

报告地点：数学科学学院114（小报告厅）  

校内联系人： 柳振鑫  教授     联系方式：84708351-8520

报告摘要：I will survey results over the last 10 years on weak convergence to Levy processes for nonuniformly hyperbolic dynamical systems. Convergence to a Levy process often holds when the central limit theorem fails. The limiting process is superdiffusive (growing like (time)^a with a>1/2) and sample paths have dense sets of discontinuities. It turns out that (in contrast to current probabilistic models) nonuniformly hyperbolic systems provide a wealth of examples that test the effectiveness (and lack of effectiveness) of the various classical Skorokhod topologies. The precise definitions are technical. Instead I'll provide examples and pictures to illustrate the theory. This is joint work with Chevyrev & Korepanov and with Freitas, Freitas & Todd.

报告人简介：Ian Melbourne, full professor at University of Warwick, UK. He got his BSc at Manchester in 1984 and PhD at Warwick in 1987 under the supervision of Ian Stewart. His research is on ergodic theory, especially with links to probability theory and stochastic analysis. Principal achievements include proving exponential decay of correlations for the classical Lorenz attractor and 1/t decay of correlations for the infinite horizon Lorentz gas, as well as giving a solution to the Wong-Zakai problem for smooth approximation of stochastic integrals of Brownian and Levy type.