Talk:Prékopa–Leindler inequality

Incorrect name for the inequality
The Prekopa-Leindler inequality is just Prekopa inequality and not Leindler, even though many people use it that way in the literure. At Prof. Prekopa's 80th birthday conference "Elliot Lieb" apologized because he was the person who named it that way. I would kindly ask author to change the title of the article to only "Prekopa inequality".

Thanks! — Preceding unsigned comment added by Merveunuvar (talk • contribs) 14:25, 31 May 2011 (UTC)

Unfortunately I don't think that's sufficient reason to cause confusion and discrepancy with the references. Did Lieb advocate everyone changing their references? 108.65.201.197 (talk) 14:42, 30 October 2012 (UTC)

Applications to probability and statistics
I added a section on the application of this inequality to probability and statistics, which I think are truly remarkable given how it relates the fundamental concepts of independence, marginalization and log-concavity. Does anyone know of other applications it has?108.65.201.197 (talk) 14:42, 30 October 2012 (UTC)

Relationship to the Brunn-Minkowski inequality
The inequality

$$\mu \left( (1 - \lambda) A + \lambda B \right) \geq \mu (A)^{1 - \lambda} \mu (B)^{\lambda},$$

mentioned as a "form" of the Brunn-Minkowski inequality

$$\mu \left( (1 - \lambda) A + \lambda B \right)^{1 / n} \geq (1 - \lambda) \mu (A)^{1 / n} + \lambda \mu (B)^{1 / n}$$

is in fact weaker since

$$ ((1 - \lambda) \mu (A)^{1 / n} + \lambda \mu (B)^{1 / n})^n \geq \mu (A)^{1 - \lambda} \mu (B)^{\lambda}$$

by the power means inequality (with powers $$ \frac 1n $$ and 0 and weights $$ 1 - \lambda $$ and $$ \lambda $$). Of course, it is still possible that the Brunn-Minkowski inequality can be deduced from the Prékopa-Leindler inequality in a more ingenious way. — Preceding unsigned comment added by Marcosaedro (talk • contribs) 15:37, 25 November 2012 (UTC)

The Brunn Minkowski article discusses this. It is now cited in the entry where you put the dubious notice. 108.65.201.197 (talk) 23:58, 28 November 2012 (UTC)