Central limit theorem for the modulus of continuity of averages of observables on transversal families of piecewise expanding unimodal maps

Abstract: We prove that the Newton quotient of the average R(t) of a lipschitzian function (with non vanishing variation) with respect to the SRB measure on a transversal family f_t of piecewise expanding unimodal maps, after an appropriated normalization, converges in distribution to the normal distribution.