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Hyperbolicity and stable polynomials in combinatorics and probability

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arxiv 1210.3231 v1 pith:Q275KV7L submitted 2012-10-11 math.CO

Robin Pemantle This is my paper · ORCID
classification math.CO
keywords theorycombinatoricslecturespolynomialsprobabilitystablebasisconference
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This was the basis of two lectures in the Current Developments in Mathematics conference in 2011. These lectures survey the theory of hyperbolic and stable polynomials, from their origins in the theory of linear PDE's to their present uses in combinatorics and probability theory.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Guessing sequences of eigenvectors for LMPs defining spectrahedral relaxations of Eulerian rigidly convex sets

    math.CO 2025-07 conditional novelty 5.0 of 10

    For even n, a carefully chosen sequence of vectors makes the spectrahedral relaxation bound for Eulerian polynomial roots exceed the univariate bound by asymptotically (3/8)(9/8)^{n/2}.

  2. Spectrahedral relaxations of Eulerian rigidly convex sets

    math.CO 2025-07 conditional novelty 5.0 of 10

    Using a multivariate spectrahedral relaxation for Eulerian polynomials produces root bounds that strictly beat the best univariate relaxation bound, but only by an exponentially small amount.

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