Hyperbolicity and stable polynomials in combinatorics and probability

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.

References in corpus (6)

• The multivariate Tutte polynomial (alias Potts model) for graphs and matroids
• Polynomials with the half-plane property and matroid theory
• Equivalent forms of the Bessis-Moussa-Villani conjecture
• A new approach to asymptotics of Maclaurin coefficients of algebraic functions
• Proof of the BMV Conjecture
• Two-dimensional quantum random walk

Cited by in corpus (4)

• Interlacing Families I: Bipartite Ramanujan Graphs of All Degrees
• Real Stable Polynomials and Matroids: Optimization and Counting
• Real Stability Testing
• On the Distribution of Critical Points of a Polynomial