Péter Nándori

Flexibility of the central limit theorem in smooth dynamical systems

We say that a diffeomorphism that preserves a smooth probability
measure satisfies the CLT if the ergodic sums of all sufficiently
smooth functions converge to a Gaussian low.
Many diffeomorphisms are known to satisfy the CLT under the usual
scaling sqrt(n). Most of these examples
also share many other chaotic properties, such as ergodicity, mixing,
positive entropy, K property, Bernoulli property.
In this talk, I will present new examples of diffeomorphisms that
satisfy the CLT but in a more exotic way. For example,
the scaling may be regularly varying with index 1, or several ergodic
properties from the above list may fail. The main idea of the
construction goes back to random walks in random sceneries. This is a
joint work with D. Dolgopyat, C. Dong and
A. Kanigowski.