The Nevai condition and a local law of large numbers for orthogonal polynomial ensembles

作者：Breuer Jonathan; Duits Maurice^*

来源：Advances in Mathematics, 2014, 265: 441-484.

DOI：10.1016/j.aim.2014.07.026

• Determinantal point processes
• Orthogonal polynomial ensembles
• Concentration inequalities
• Local law of large numbers
• Orthogonal polynomials
• Nevai condition

We consider asymptotics of orthogonal polynomial ensembles, in the macroscopic and mesoscopic scales. We prove both global and local laws of large numbers under fairly weak conditions on the underlying measure mu. 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.

• 出版日期2014-11-10