Let be a family of random independent k-element subsets of [n] = 1,2,...,n and let denote a family of ℓ-element subsets of [n] such that the event that S belongs to depends only on the edges of contained in S. Then, the edges of are ’weakly dependent’, say, the events that two given subsets S and T are in are independent for vast majority of pairs S and T. In the paper we present some results on the structure of weakly dependent families of subsets obtained in this way. We also list some questions which, despite the progress which has been made for the last few years, remain to puzzle researchers who work in the area of probabilistic combinatorics.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc95-0-9,
author = {Tomasz \L uczak},
title = {On families of weakly dependent random variables},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {123-132},
zbl = {1238.05250},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc95-0-9}
}
Tomasz Łuczak. On families of weakly dependent random variables. Banach Center Publications, Tome 95 (2011) pp. 123-132. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc95-0-9/