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Negative dependence and the geometry of polynomials
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
2009 (English)In: Journal of The American Mathematical Society, ISSN 0894-0347, E-ISSN 1088-6834, ., Vol. 22, no 2, 521-567 p.Article in journal (Refereed) Published
Abstract [en]

We introduce the class of strongly Rayleigh probability measures by means of geometric properties of their generating polynomials that amount to the stability of the latter. This class covers important models such as determinantal measures (e.g. product measures and uniform random spanning tree measures) and distributions for symmetric exclusion processes. We show that strongly Rayleigh measures enjoy all virtues of negative dependence, and we also prove a series of conjectures due to Liggett, Pemantle, and Wagner, respectively. Moreover, we extend Lyons' recent results on determinantal measures, and we construct counterexamples to several conjectures of Pemantle and Wagner on negative dependence and ultra log-concave rank sequences.

Place, publisher, year, edition, pages
2009. Vol. 22, no 2, 521-567 p.
Keyword [en]
Negative association, stable polynomials, hyperbolic polynomials, determinants, matrices, spanning trees, matroids, probability measures, stochastic domination, interacting particle systems, exclusion processes
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-21685DOI: 10.1090/S0894-0347-08-00618-8OAI: oai:DiVA.org:su-21685DiVA: diva2:188212
Available from: 2008-11-11 Created: 2008-11-11 Last updated: 2017-12-13Bibliographically approved

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Publisher's full texthttp://arxiv.org/abs/0707.2340

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