Negative correlation and log-concavity

Details Negative correlation and log-concavity Negative correlation and log-concavity

2007-12-20

arxiv.org/abs/0712.3507v3

Mathematics

Probability

21 pages; only minor changes since previous version; accepted for publication in Random Structures and Algorithms

Scientific paper

We give counterexamples and a few positive results related to several conjectures of R. Pemantle and D. Wagner concerning negative correlation and log-concavity properties for probability measures and relations between them. Most of the negative results have also been obtained, independently but somewhat earlier, by Borcea et al. We also give short proofs of a pair of results due to Pemantle and Borcea et al.; prove that "almost exchangeable" measures satisfy the "Feder-Mihail" property, thus providing a "non-obvious" example of a class of measures for which this important property can be shown to hold; and mention some further questions.

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