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May 25, 2022 at 14:25 vote accept Enguerrand Moulinier
May 25, 2022 at 13:01 comment added Iosif Pinelis @EnguerrandMoulinier : Corollary 3.2 is proved by Bobkov and Madiman, on p. 1534, just before Corollary 3.2 is stated. There is a small, easily correctable mistake in that proof, though: the log-linear (in $p$) factor $n^{p+1}$ should be replaced by the log-linear factor $n^p$. So, can we now finalize this matter in accordance with the MathOverflow guidelines at mathoverflow.net/help/accepted-answer and mathoverflow.net/help/someone-answers ?
May 25, 2022 at 7:58 comment added Enguerrand Moulinier Thank you for your answer. What saddens me is that the corollary 3.2 is left unproven and seems hard to prove. I wonder why the inequality on those log concave variables isn't more known since it shows up when working with beta variables wich are quite commons.
May 18, 2022 at 20:36 history answered Iosif Pinelis CC BY-SA 4.0