2020/06/03 by Peter J. Forrester, Santosh Kumar, Forrester, Peter J. +1
Mathematics · #11B37 #15A18 #15B52 #33C45 #60B20 #65Qxx #Advanced Algebra and Geometry #Computation (stat.CO) #Data Analysis #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.2006.02238
openalex publication_date 2020/06/03 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
The Jacobi ensemble is one of the classical ensembles of random matrix theory. Prominent in applications are properties of the eigenvalues at the spectrum edge, specifically the distribution of the largest (e.g. Roy's largest root test in multivariate statistics) and smallest (e.g.~condition numbers of linear systems) eigenvalues. We identify three ranges of parameter values for which the gap probability determining these distributions is a finite sum with respect to particular bases, and moreover make use of a certain differential-difference system fundamental in the theory of the Selberg integral to provide a recursive scheme to compute the corresponding coefficients.