確率論セミナー


2017/11/7(Tue)

16:30--18:00 数学教室 大セミナー室 (E404)

Freddy Delbaen

Prof. em. at the Department of Mathematics, ETH Zurich. and Visiting Professor at the Institute of Mathematics of the University of Zurich

A generalisation of a result of Mark Kac (Ann.Maths. 47 (1946))

In 1946 Mark Kac proved that for a centred Hoelder continuous function $f$ defined on $[0,1]$ and extended periodically to the whole real line, the sequence $f(2^k t)$ satisfies a Central Limit Theorem. We extend the result to measurable $L^2$ functions satisfying a fast approximation property. The result naturally extends to similar functions defined on Bernoulli shifts.

Joint work with Emma Hovhannisyan and Ashkan Nikeghbali (both from the University of Zurich).