STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Balls and bins: a study in negative dependence
Random Structures & Algorithms
Combinatorics, Probability and Computing
Negative correlation and log-concavity
Random Structures & Algorithms
A strong log-concavity property for measures on Boolean algebras
Journal of Combinatorial Theory Series A
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We prove conditional negative association for random variables xj = 1**math-image** (j∈[n]:= {1…n}) , where σ(1)…σ(m) are i.i.d. from [n]. (The σ(i) 's are thought of as the locations of balls dropped independently into urns 1…n according to some common distribution, so that, for some threshold tj, xj is the indicator of the event that at least tj balls land in urn j.) We mostly deal with the more general situation in which the σ(i) 's need not be identically distributed, proving results which imply conditional negative association in the i.i.d. case. Some of the results—particularly Lemma 8 on graph orientations—are thought to be of independent interest. We also give a counterexample to a negative correlation conjecture of D. Welsh, a strong version of a (still open) conjecture of G. Farr. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012 © 2012 Wiley Periodicals, Inc.