Asymptotic zero distribution of Jacobi-Pi\~neiro and multiple Laguerre polynomials

TL;DR

This paper determines the asymptotic zero distribution of Jacobi-Pineiro and multiple Laguerre polynomials, linking their zeros to Fuss-Catalan distribution using recurrence relations and ratio asymptotics.

Contribution

It provides the first detailed analysis of the asymptotic zero distribution for these classes of multiple orthogonal polynomials, connecting them to Fuss-Catalan distribution.

Findings

Zeros asymptotically follow Fuss-Catalan distribution

Recurrence relations are key to analyzing zero distribution

Ratio asymptotics facilitate the asymptotic analysis

Abstract

We give the asymptotic distribution of the zeros of Jacobi-Pi\~neiro polynomials and multiple Laguerre polynomials of the first kind. We use the nearest neighbor recurrence relations for these polynomials and a recent result on the ratio asymptotics of multiple orthogonal polynomials. We show how these asymptotic zero distributions are related to the Fuss-Catalan distribution.