Aizenman's Theorem for Orthogonal Polynomials on the Unit Circle

Simple item page
dc.creatorSimon, Barry
dc.date2004-11-17
dc.date.accessioned2026-07-07T05:14:25Z
dc.date.available2026-07-07T05:14:25Z
dc.descriptionFor suitable classes of random Verblunsky coefficients, including independent, identically distributed, rotationally invariant ones, we prove that if \[ \mathbb{E} \biggl(\int\frac{dθ}{2π} \biggl|\biggl(\frac{\mathcal{C} + e^{iθ}}{\mathcal{C} -e^{iθ}} \biggr)_{k\ell}\biggr|^p \biggr) \leq C_1 e^{-κ_1 |k-\ell|} \] for some $κ_1 >0$ and $p<1$, then for suitable $C_2$ and $κ_2 >0$, \[ \mathbb{E} \bigl(\sup_n |(\mathcal{C}^n)_{k\ell}|\bigr) \leq C_2 e^{-κ_2 |k-\ell|} \] Here $\mathcal{C}$ is the CMV matrix.
dc.descriptionKeywords: OPUC, random Verblunsky coefficients, localization
dc.identifierhttps://arxiv.org/abs/math/0411388
dc.identifierhttp://arxiv.org/abs/math/0411388
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73270
dc.subjectSpectral Theory
dc.subject26C05, 82B44, 47N20
dc.titleAizenman's Theorem for Orthogonal Polynomials on the Unit Circle
dc.typetext

Files

Collections

arXiv