2024/04/11 by Grzegorz Świderski, Świderski, Grzegorz
Mathematics · #42C05 (Primary) 47B36 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Probability (math.PR) #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2404.07566
openalex publication_date 2024/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
We study Nevai's condition from the theory of orthogonal polynomials on the real line. We prove that a large class of measures with unbounded Jacobi parameters satisfies Nevai's condition locally uniformly on the support of the measure away from a finite explicit set. This allows us to give applications to relative uniform and weak asymptotics of Christoffel-Darboux kernels on the diagonal and to limit theorems for unconventionally normalized global linear statistics of orthogonal polynomial ensembles.