Multihomogenous Nonnegative Polynomials and Sums of Squares

TL;DR

This paper refines bounds on the proportion of multihomogeneous nonnegative polynomials that can be expressed as sums of squares, advancing understanding in polynomial nonnegativity and sum of squares representations.

Contribution

It extends and refines existing bounds to the multihomogeneous case, providing new quantitative insights into nonnegative polynomials and sums of squares.

Findings

Improved bounds for multihomogeneous polynomials

Quantitative analysis of sum of squares representations

Enhanced understanding of polynomial nonnegativity

Abstract

We refine and extend quantitative bounds, on the fraction of nonnegative polynomials that are sums of squares, to the multihomogenous case.