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Limit theorems for random Lasota-Yorke maps using the spectral method

The so-called Nagaev-Guivarc’h spectral method is one of the most powerful tools in establishing limit theorems and has been successfully applied in various situations including Markov chains and dynamical systems. In the standard deterministic setting the method consists of finding an appro- priate Banach space on which the transfer opera- tor has a spectral gap and then applying various results from the perturbation theory of linear op- erators. In this talk, I will discuss an ongoing research project which aims to extend this method to the random case. We will also explain how the multi- plicative ergodic theorem naturally appears in this setting. This is a joint work with G. Froyland, C. Gonz ́alez Tokman and S. Vaienti.

limit theorems; random dynamical systems

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