Marta Tyran-Kaminska
Title: Convergence to Levy stable processes and inducing

Abstract: Properly normalized Birkhoff sums might converge in distribution to stable laws. Such limit theorems are known for example in a class of heavy-tailed observables of Gibbs-Markov maps. Inducing on a properly chosen set in a given system can lead to a nice induced map and with some extra work one can prove a limit theorem for the original system as was the case with intermittent maps. I will discuss the problem of proving limit theorems in the original system if we know that convergence to Levy stable processes holds in an induced system and vice versa.