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Abstract: In this talk, I present random tower maps driven by an ergodic automorphism and prove quenched exponential correlations decay for tower maps admitting exponential tails. The technique is based on constructing suitable cones of functions, defined on the random towers, which contract with respect to the Hilbert metric under the action of appropriate transfer operators. This is joint work with J.Alves, W.Bahsoun and P.Varandas.