Negative dependence and the geometry of polynomials

Author:

Borcea Julius,Brändén Petter,Liggett Thomas

Abstract

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference74 articles.

1. On the generating functions of totally positive sequences. I;Aissen, Michael;J. Analyse Math.,1952

2. A correlation inequality for the symmetric exclusion process;Andjel, Enrique D.;Ann. Probab.,1988

3. Lacunas for hyperbolic differential operators with constant coefficients. I;Atiyah, M. F.;Acta Math.,1970

4. Hyperbolic polynomials and convex analysis;Bauschke, Heinz H.;Canad. J. Math.,2001

5. Determinantal processes and independence;Hough, J. Ben;Probab. Surv.,2006

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