### Flexibility of the central limit theorem in smooth dynamical systems

Probability Seminar

23rd February 2022, 4:00 pm – 5:00 pm

Online,

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.

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