Abstract
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 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.
Original language | English |
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Pages (from-to) | 441-484 |
Number of pages | 44 |
Journal | Advances in Mathematics |
Volume | 265 |
DOIs | |
State | Published - 10 Nov 2014 |
Keywords
- Concentration inequalities
- Determinantal point processes
- Local law of large numbers
- Nevai condition
- Orthogonal polynomial ensembles
- Orthogonal polynomials
All Science Journal Classification (ASJC) codes
- General Mathematics