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

Yoram Last*, Barry Simon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

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 priori bounds on eigenvalue spacings for which we provide several proofs.

Original languageAmerican English
Pages (from-to)486-538
Number of pages53
JournalCommunications on Pure and Applied Mathematics
Volume61
Issue number4
DOIs
StatePublished - Apr 2008

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