QUENCHED DECAY OF CORRELATIONS FOR SLOWLY MIXING SYSTEMS

We study random towers that are suitable to analyse the statistics of slowly mixing random systems. We obtain upper bounds on the rate of quenched correlation decay in a general setting. We apply our results to the random family of Liverani-Saussol-Vaienti maps with parameters in [alpha(0), alpha(1)] subset of (0, 1) chosen independently with respect to a distribution nu on [alpha(0), alpha(1)] and show that the quenched decay of correlation is governed by the fastest mixing map in the family. In particular, we prove that for every delta > 0, for almost every omega is an element of[alpha(0), alpha(1)](Z), the upper bound n(1)-1/alpha(0) +delta holds on the rate of decay of correlation for Holder observables on the fibre over omega. For three different distributions nu on [alpha(0), alpha(1)] (discrete, uniform, quadratic), we also derive sharp asymptotics on the measure of return-time intervals for the quenched dynamics, ranging from n-1/alpha(0) to (log n) 1/alpha(0) center dot n-1/alpha(0) to (log n) 2/alpha(0) . n -1/alpha(0,) respectively.