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Exponential law for random subshifts of finite type

In this paper we study the distribution of hitting times for a class of random dynamical systems. We prove that for invariant measures with super-polynomial decay of correlations hitting times to dynamically defined cylinders satisfy exponential distribution. Similar results are obtained for ran- dom expanding maps. We emphasize that what we establish is a quenched exponential law for hitting times.

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Benoit Saussol