Asymptotic zero distribution of Jacobi-Piñeiro and multiple Laguerre polynomials

Abstract

We give the asymptotic distribution of the zeros of Jacobi-Piñeiro 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.

arXiv comment19 pages, 2 figures. Some minor corrections and four new references added

References in corpus (9)

• Some classical multiple orthogonal polynomials
• Product of Ginibre matrices: Fuss-Catalan and Raney distributions
• Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits
• The nearest neighbor recurrence coefficients for multiple orthogonal polynomials
• Raney distributions and random matrix theory
• Interlacing properties of zeros of multiple orthogonal polynomials
• Mehler-Heine asymptotics for multiple orthogonal polynomials
• Random matrix minor processes related to percolation theory
• Ratio asymptotics for multiple orthogonal polynomials

Cited by in corpus (7)

• Laguerre-Angelesco multiple orthogonal polynomials on an $r$-star
• A Vector Equilibrium Problem for Muttalib-Borodin Biorthogonal Ensembles
• Electrostatic partners and zeros of orthogonal and multiple orthogonal polynomials
• Multiple Orthogonal Polynomials and Random Walks
• Jacobi-Angelesco multiple orthogonal polynomials on an $r$-star
• Christoffel functions for multiple orthogonal polynomials
• Szegő Recurrence for Multiple Orthogonal Polynomials on the Unit Circle