Recently, the study of the statistical properties of
non-autonomous dynamical systems has gained increased interest, with a
particular emphasis on the property of loss of memory, which is the
generalization of the classical notion of decay of correlations: if we
start from two probability densities, both belonging to a class of
smooth enough functions, and if we let them evolve with the dynamic,
they will be attracted one from each other if the system is su
fficiently mixing. A natural question is then to estimate the speed of
loss of memory, a question which was investigated thoroughly for
systems with uniform expansion/hyperbolicity and whence enjoying a
loss of memory with exponential rate. During this talk, I will present
a result for a system consisting of intermittent maps of the unit
interval, sharing a common neutral fixed point, for which the loss of
memory occurs at a polynomial rate. If time permits, I will also
present results on finer statistical properties, such as the central
limit theorem and concentration inequalities, in the case of non
autonomous systems with exponential loss of memory.