Alexey Korepanov

Title: Strength of strong approximation with a Brownian motion.

Abstract: Motion of a particle in Lorentz gas can be strongly (almost
surely) approximated by a Brownian motion. Such an approximation implies
the functional central limit theorem, the functional law of iterated
logarithm, the almost sure central limit theorem and other useful
things. A particularly challenging problem in both dynamical systems and
probability theory is control of the approximation error. I will present
recent new results for dynamical systems such as the doubling map, Axiom
A diffeomorphisms, logistic maps or Lorentz gas. Joint work (in
progress) with C.Cuny, J.Dedecker and F.Merlevede.