Institute of Mathematics


Modul:   MAT760  Ergodic theory and dynamical systems seminar

A central limit theorem for irrational rotations of bounded type

Talk by Dr. Hao Wu

Date: 06.03.24  Time: 13.30 - 14.30  Room: ETH HG G 19.1

In hyperbolic dynamical systems, one can often prove the spatial central limit theorem (CLT), where the starting point is randomized with respect to the SRB measures. In zero-entropy systems such as irrational rotations, the spatial CLT often fails due to lack of mixing properties. However, using coding and Markov chains, Bromberg and Ulcigrai showed that a temporal CLT holds for bounded type irrational rotations with step functions whose jump point lies in a full Hausdorff dimension set. Here "temporal" means that we randomise time while fixing the starting point. In an ongoing joint work with Bromberg and Ulcigrai, we extend this result from full Hausdorff dimension to full Lebesgue measure.