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Liverani-Saussol-Vaienti (L-S-V) maps form a family of piecewisedifferentiable dynamical systems on $[0,1]$ depending on one parameter$\omega\in\mathbb R^+$. These maps are everywhere expanding apart from aneutral fixed point. It is well known that depending on the amount of expansionclose to the neutral point, they have either an absolutely continuous invariantprobability measure and polynomial decay of correlations ($\omega <1$), or aunique physical measure that is singular and concentrated at the neutral point($\omega >1$). In this paper, we study the composition of L-S-V maps whoseparameters are randomly sampled from a range in $\mathbb R^+$, and where thesetwo contrasting behaviours are mixed. We show that if the parameters $\omega<1$are sampled with positive probability, then the stationary measure of therandom system is absolutely continuous; the annealed decay rate of correlationsis close (or in some cases equal) to the fastest rate of decay among those ofthe sampled systems; and suitably rescaled Birkhoff averages converge to limitlaws. In contrast to previous studies where $\omega \in [0,1]$, we allow $\omega >1$ in our sampling distribution. We also show that one can obtainsimilar decay of correlation rates for $\omega \in [0,\infty)$, when samplingis done with respect to a family of smooth, heavy-tailed distributions.

Random Composition of L-S-V Maps Sampled Over Large Parameter Ranges