2013/11/02 by Thorsten Neuschel, Neuschel, Thorsten · 3 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Probability (math.PR) #Random Matrices and Applications #math-ph #math.CA #math.MP #math.PR
paper · pdf · doi:10.48550/arxiv.1311.0365
18 pages
arxiv created 2013/11/02 · openalex publication_date 2013/11/02 · arxiv updated 2013/11/05 · openalex created_date 2022/08/13 · openalex updated_date 2026/07/28
Formulae of Plancherel-Rotach type are established for the average characteristic polynomials of certain Hermitian products of rectangular Ginibre random matrices on the region of zeros. These polynomials form a general class of multiple orthogonal hypergeometric polynomials generalizing the classical Laguerre polynomials. The proofs are based on a multivariate version of the complex method of saddle points. After suitable rescaling the asymptotic zero distributions for the polynomials are studied and shown to coincide with the Fuss-Catalan distributions. Moreover, introducing appropriate coordinates, elementary and explicit characterizations are derived for the densities as well as for the distribution functions of the Fuss-Catalan distributions of general order.