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18805

A Productization Property/Trick For H-Stable(And Hopefully Strongly Log-Concave) Polynomials

APA

(2021). A Productization Property/Trick For H-Stable(And Hopefully Strongly Log-Concave) Polynomials. The Simons Institute for the Theory of Computing. https://simons.berkeley.edu/talks/productization-propertytrick-h-stableand-hopefully-strongly-log-concave-polynomials

Leonid Gurvits (City College of New York)
Talk number18805
Source RepositorySimons Institute

Abstract

The simplest homogeneous polynomials with nonnegative coefficients are products of linear forms Prod_{A}(X) associated with nonnegative matrices A. We prove that for any H-Stable(homogeneous and stable) polynomial p with P(E) = 1, where E is the vector of all ones, it's value p(X) = Prod_{A(X)}(X), where A(X) is nonnegative matrix with unit row sums and the vector of column sums equal to the gradient of p at E. I will first explain some intuition, and history, behind the result; sketch the proof and present a few applications and generalizations of this "productization" property. (Joint work with Jonathan Leake).