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 Euclidean balls. This solves a conjecture of June Huh and the author. The proof utilises and refines a connection between the symmetric exclusion process in interacting particle systems and the geometry of polynomials.

Keywords

• Lorentzian polynomial
• Stable polynomial
• Symmetric exclusion process
• Euclidean ball
• 52B40
• 05E14
• 60J27