José Alves: From decay of correlations to large deviations

We will obtain some estimates on the large deviations from the decay of correlations of certain classes of dynamical systems. From that we will deduce some statistical properties for families of generalized Viana maps, namely Viana maps with beta transformations or quadratic transformations as the base map of the skew-product. The first part is joint work with J. Freitas, S. Luzzatto and S. Vaienti and the second one is joint work with D. Schnellmann.