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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Negative dependence and the geometry of polynomials
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by Julius Borcea, Petter Brändén and Thomas M. Liggett PDF
J. Amer. Math. Soc. 22 (2009), 521-567 Request permission

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.
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Additional Information
  • Julius Borcea
  • Affiliation: Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden
  • Email: julius@math.su.se
  • Petter Brändén
  • Affiliation: Department of Mathematics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
  • MR Author ID: 721471
  • Email: pbranden@math.kth.se
  • Thomas M. Liggett
  • Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095-1555
  • Email: tml@math.ucla.edu
  • Received by editor(s): July 17, 2007
  • Published electronically: September 19, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 22 (2009), 521-567
  • MSC (2000): Primary 62H20; Secondary 05B35, 15A15, 15A22, 15A48, 26C10, 30C15, 32A60, 60C05, 60D05, 60E05, 60E15, 60G55, 60K35, 82B31
  • DOI: https://doi.org/10.1090/S0894-0347-08-00618-8
  • MathSciNet review: 2476782