Capacity of Lorentzian polynomials and distance to binomial distributions

TL;DR

This paper investigates the capacity of Lorentzian polynomials using a probabilistic approach, providing a new proof of a known theorem and exploring the relationship between binomial distributions and fixed expectations.

Contribution

It introduces a novel probabilistic proof of a theorem on Lorentzian polynomial capacity, connecting it to binomial distribution distances.

Findings

New probabilistic proof of Bränden, Leake, and Pak's theorem

Establishes a link between binomial distribution distances and polynomial capacity

Provides insights into the structure of Lorentzian polynomials

Abstract

In this paper we study the capacity of Lorentzian polynomials. We give a new proof of a theorem of Br\"and\'en, Leake and Pak. Our approach is probabilistic in nature and uses a lemma about a certain distance of binomial distributions to distributions with fixed expected value.