### Skapa referens, olika format (klipp och klistra)

**Harvard**

van den Berg, J. och Jonasson, J. (2012) *A BK inequality for randomly drawn subset of fixed size*.

** BibTeX **

@article{

van den Berg2012,

author={van den Berg, Jacob and Jonasson, Johan},

title={A BK inequality for randomly drawn subset of fixed size},

journal={Probability Theory and Related Fields},

issn={0178-8051},

volume={154},

issue={3-4},

pages={835-844 },

abstract={The BK inequality (van den Berg and Kesten in J Appl Probab 22:556–569, 1985) says that, for product measures on {0, 1} n , the probability that two increasing events A and B ‘occur disjointly’ is at most the product of the two individual probabilities. The conjecture in van den Berg and Kesten (1985) that this holds for all events was proved by Reimer (Combin Probab Comput 9:27–32, 2000). Several other problems in this area remained open. For instance, although it is easy to see that non-product measures cannot satisfy the above inequality for all events, there are several such measures which, intuitively, should satisfy the inequality for all increasing events. One of the most natural candidates is the measure assigning equal probabilities to all configurations with exactly k 1’s (and probability 0 to all other configurations). The main contribution of this paper is a proof for these measures. We also point out how our result extends to weighted versions of these measures, and to products of such measures.},

year={2012},

keywords={BK inequality, negative dependence},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 149578

A1 van den Berg, Jacob

A1 Jonasson, Johan

T1 A BK inequality for randomly drawn subset of fixed size

YR 2012

JF Probability Theory and Related Fields

SN 0178-8051

VO 154

IS 3-4

SP 835

OP 844

AB The BK inequality (van den Berg and Kesten in J Appl Probab 22:556–569, 1985) says that, for product measures on {0, 1} n , the probability that two increasing events A and B ‘occur disjointly’ is at most the product of the two individual probabilities. The conjecture in van den Berg and Kesten (1985) that this holds for all events was proved by Reimer (Combin Probab Comput 9:27–32, 2000). Several other problems in this area remained open. For instance, although it is easy to see that non-product measures cannot satisfy the above inequality for all events, there are several such measures which, intuitively, should satisfy the inequality for all increasing events. One of the most natural candidates is the measure assigning equal probabilities to all configurations with exactly k 1’s (and probability 0 to all other configurations). The main contribution of this paper is a proof for these measures. We also point out how our result extends to weighted versions of these measures, and to products of such measures.

LA eng

DO 10.1007/s00440-011-0386-z

LK http://dx.doi.org/10.1007/s00440-011-0386-z

OL 30