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)

TL;DR

This paper addresses and corrects specific flaws in the proofs of Theorem 3.2 and Corollary 5.2 from a 2002 paper on mixing rates of unimodal maps, clarifying the validity of the results.

Contribution

The authors provide corrected proofs for key results in their previous work, ensuring the mathematical accuracy of their findings on mixing rates.

Findings

Corrected proof of Theorem 3.2 without claims on lower bounds

Adjusted proof of Corollary 5.2 with a smaller set replacement

Confirmation of the main results' validity after corrections

Abstract

In 2010, Weixiao Shen pointed out to us that the proof of Theorem 3.2 of our 2002 paper in Ann ENS was flawed, and he kindly provided an argument to fix this proof. (We do not make claims on the lower bounds for the stationary density anymore.) In 2017, Wael Bahsoun, Christopher Bose, and Marks Ruziboev pointed 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. 93 by a slightly smaller set (this does not affect the rest of the paper).