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arXiv · 1904.11552

A rectangular additive convolution for polynomials

Aurelien Gribinski·Adam W. Marcus
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Abstract

We define the rectangular additive convolution of polynomials with nonnegative real roots as a generalization of the asymmetric additive convolution introduced by Marcus, Spielman and Srivastava. We then prove a sliding bound on the largest root of this convolution. The main tool used in the analysis is a differential operator derived from the "rectangular Cauchy transform" introduced by Benaych-Georges. The proof is inductive, with the base case requiring a new nonasymptotic bound on the Cauchy transform of Gegenbauer polynomials which may be of independent interest.

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Aurelien Gribinski, Adam W. Marcus. 2022-02-25. A rectangular additive convolution for polynomials. https://arxiv.org/abs/1904.11552

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