Seminar in Trieste: Ian Melbourne

Wednesday 17th August at 14:30 (ICTP)

“Martingale approximation for parametrised dynamical systems”

Abstract: In joint work with Alexey Korepanov and Zemer Kosloff, we prove statistical limit laws for sequences of the type \(\sum_{j=0}^{n-1}v_n\circ T_n^j\) where \(T_n\) is a family of nonuniformly hyperbolic transformations.  The key ingredient is a new martingale-coboundary decomposition for nonuniformly hyperbolic transformations which is useful in the case when the family \(T_n\) is replaced by a fixed transformation \(T\), but which is particularly useful in the case when \(T_n\) varies with \(n\).