2013/01/10 by Jonathan Breuer, Breuer, Jonathan, Maurice Duits +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR
paper · pdf · doi:10.48550/arxiv.1301.2061
44 pages
openalex publication_date 2013/01/10 · arxiv created 2013/01/11 · arxiv updated 2013/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider asymptotics of orthogonal polynomial ensembles, in the macroscopic and mesoscopic scales. We prove both global and local laws of large numbers (analogous to the recently proven local semicircle law for Wigner matrices) under fairly weak conditions on the underlying measure μ. Our main tools are a general concentration inequality for determinantal point processes with a kernel that is a self-adjoint projection, and a strengthening of the Nevai condition from the theory of orthogonal polynomials.