Negative association for a family of random variables means that for any coordinatewise increasing functions f,g we have for any disjoint sets of indices (iₘ), (jₙ). It is a way to indicate the negative correlation in a family of random variables. It was first introduced in 1980s in statistics by Alem Saxena and Joag-Dev Proschan, and brought to convex geometry in 2005 by Wojtaszczyk Pilipczuk to prove the Central Limit Theorem for Orlicz balls. The paper gives a relatively simple proof of negative association of absolute values for a wide class of measures tied to generalized Orlicz balls, including the uniform measures on such balls.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-1-5,
author = {Jakub Onufry Wojtaszczyk},
title = {A Simpler Proof of the Negative Association Property for Absolute Values of Measures Tied to Generalized Orlicz Balls},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {57},
year = {2009},
pages = {41-56},
zbl = {1172.52007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-1-5}
}
Jakub Onufry Wojtaszczyk. A Simpler Proof of the Negative Association Property for Absolute Values of Measures Tied to Generalized Orlicz Balls. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) pp. 41-56. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-1-5/