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