Fine Structure of the Zeros of Orthogonal Polynomials, IV. A Priori Bounds and Clock Behavior

By Yoram Last, Barry Simon. 2006

49 citations recorded by the source corpus.

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 Schrodinger operators, Poisson behavior implies positive Lyapunov exponent. Both results depend on a priori bounds on eigenvalue spacings for which we provide several proofs.

View Paper: https://www.semanticscholar.org/paper/8daf07f084589acb33e473c2880c2af426752ce0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Barry Simon
2. David Damanik
3. Rowan Killip
4. Doron S. Lubinsky
5. N. H. Bingham
6. Sergey A. Denisov
7. Dan Romik
8. J. Toft

Citations in the corpus

• The Christoffel-Darboux Kernel (2008, methodology): “The following theorem of Last–Simon [57], based on ideas of Golinskii [41], can be used on successive zeros (see [57] for the proof).”