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We consider asymptotics of orthogonal polynomial ensembles, in themacroscopic and mesoscopic scales. We prove both global and local laws of largenumbers (analogous to the recently proven local semicircle law for Wignermatrices) under fairly weak conditions on the underlying measure $\mu$. Ourmain tools are a general concentration inequality for determinantal pointprocesses with a kernel that is a self-adjoint projection, and a strengtheningof the Nevai condition from the theory of orthogonal polynomials.

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