Hyperbolicity and stable polynomials in combinatorics and probability

2012/10/11 by Pemantle, Robin
#05A15 #26C10 #62H20 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1210.3231

Abstract

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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• Aspects of stable polynomials
• Multivariate stable polynomials: theory and applications
• Testing hyperbolicity of real polynomials
• Searching for Hyperbolicity
• Hyperbolic polynomials and the Marcus-Spielman-Srivastava theorem