2008/05/23 by E. Ryckman
Mathematics · Physics and Astronomy · #Classical orthogonal polynomials #Discrete orthogonal polynomials #Gegenbauer polynomials #Jacobi polynomials #Joint probability distribution #Limit (mathematics) #Mathematical functions and polynomials #Mehler–Heine formula #Orthogonal polynomials #Point process #Point processes and geometric inequalities #Random Matrices and Applications #Wilson polynomials #math-ph #math.MP #math.PR
paper · pdf · doi:10.1007/s10955-008-9564-5
Added references, corrected typos. To appear, J. Stat. Phys
arxiv created 2008/05/23 · openalex publication_date 2008/05/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
For arbitrary β> 0, we use the orthogonal polynomials techniques developed by R. Killip and I. Nenciu to study certain linear statistics associated with the circular and Jacobi β ensembles. We identify the distribution of these statistics then prove a joint central limit theorem. In the circular case, similar statements have been proved using different methods by a number of authors. In the Jacobi case these results are new.