Spaces of Lorentzian and real stable polynomials are Euclidean balls

Abstract

We prove that projective spaces of Lorentzian and real stable polynomials are homeomorphic to closed Euclidean balls. This solves a conjecture of June Huh and the author. The proof utilizes and refines a connection between the symmetric exclusion process in Interacting Particle Systems and the geometry of polynomials.

arXiv commentFixed some issues with compactness in the case of real stable polynomials

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Cited by in corpus (2)

• Gradient flows, adjoint orbits, and the topology of totally nonnegative flag varieties
• On complete classes of valuated matroids