# Fine structure of the zeros of orthogonal polynomials IV: A priori bounds and clock behavior

@article{Last2006FineSO, title={Fine structure of the zeros of orthogonal polynomials IV: A priori bounds and clock behavior}, author={Yoram Last and Barry Simon}, journal={Communications on Pure and Applied Mathematics}, year={2006}, volume={61} }

We prove locally uniform spacing for the zeros of orthogonal polynomials on the real line under weak conditions (Jacobi parameters approach the free ones and are of bounded variation). We prove that for ergodic discrete Schrödinger operators, Poisson behavior implies a positive Lyapunov exponent. Both results depend on a priori bounds on eigenvalue spacings for which we provide several proofs. © 2007 Wiley Periodicals, Inc.

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