  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 $\mu$. 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.
