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In 2010, Weixiao Shen pointed out to us that the proof of Theorem 3.2 of our2002 paper in Ann ENS was flawed, and he kindly provided an argument to fixthis proof. (We do not make claims on the lower bounds for the stationarydensity anymore.) In 2017, Wael Bahsoun, Christopher Bose, and Marks Ruziboevpointed out to us that the proof of Corollary 5.2 in the same paper is flawed.We explain how to recover Corollary 5.2 up to replacing the set $M'_q$ on p. 93by a slightly smaller set (this does not affect the rest of the paper).

Correcting the proof of Theorem 3.2 and Corollary 5.2 in Almost sure  rates of mixing for i.i.d. unimodal maps by V. Baladi, M. Benedicks, V.  Maume-Deschamps, Ann. E.N.S. (2002)