Spaces of Lorentzian and real stable polynomials are Euclidean balls

TL;DR

This paper proves that certain spaces of Lorentzian and real stable polynomials are topologically equivalent to Euclidean balls, confirming a conjecture and linking polynomial geometry with particle system dynamics.

Contribution

It establishes the homeomorphism between polynomial spaces and Euclidean balls, solving a conjecture and connecting polynomial stability with particle system geometry.

Findings

Spaces of Lorentzian and real stable polynomials are homeomorphic to Euclidean balls.

The proof refines the connection between polynomial geometry and the symmetric exclusion process.

The conjecture by June Huh and the author is confirmed.

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.