# Annealed and quenched central limit theorem for random dynamical systems

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Romain Aimino

created by daniele on 07 Dec 2015

9 dec 2015
-- 14:30

Aula Riunioni, Collegio Puteano, CRM, Pisa

Seminari di Sistemi Dinamici Olomorfi, Pisa

**Abstract.**

For random dynamical systems, one can distinguish two kinds of limit
theorems: annealed results, which refer to the Birkhoff sums seen as
functions of both the phase space variable and the choice of the maps
composed, and quenched results, which refer to Birkhoff sums for a fixed,
but generic, composition of maps. In this talk, I will describe results
about the central limit theorem for random dynamical systems consisting of
uniformly expanding maps. In particular, I will show that the annealed
central limit theorem is valid for such systems, and I will give a
necessary and sufficient condition for its quenched version without random
centering to hold. This is a joint work with Matthew Nicol and Sandro
Vaienti.