Negative dependence and the geometry of polynomials

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dc.creatorBorcea, Julius
dc.creatorBrändén, Petter
dc.creatorLiggett, Thomas M.
dc.date2007-07-16
dc.date2008-07-27
dc.date.accessioned2026-07-07T12:36:40Z
dc.date.available2026-07-07T12:36:40Z
dc.descriptionWe introduce the class of {\em 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, 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.
dc.descriptionFinal version, to appear in J. Amer. Math. Soc.; 47 pages, 1 figure, LaTeX2e
dc.identifierhttps://arxiv.org/abs/0707.2340
dc.identifierhttp://arxiv.org/abs/0707.2340
dc.identifierJ. Amer. Math. Soc. 22 (2009), 521-567.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/218169
dc.subjectProbability
dc.subjectMathematical Physics
dc.subjectCombinatorics
dc.subject62H20 (Primary) 05B35, 15A15, 30C15, 32A60, 60E15, 60K35, 82B31 (Secondary)
dc.titleNegative dependence and the geometry of polynomials
dc.typetext

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