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.

Fixed some issues with compactness in the case of real stable polynomials

References in corpus (2)

• Total positivity, Grassmannians, and networks
• Regularity theorem for totally nonnegative flag varieties

Cited by in corpus (2)

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