Aizenman's Theorem for Orthogonal Polynomials on the Unit Circle

Simon, Barry (2006) Aizenman's Theorem for Orthogonal Polynomials on the Unit Circle. Constructive Approximation, 23 (2). pp. 229-240. ISSN 0176-4276. doi:10.1007/s00365-005-0599-4. https://resolver.caltech.edu/CaltechAUTHORS:20170726-134636444

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Abstract

For suitable classes of random Verblunsky coefficients, including independent, identically distributed, rotationally invariant ones, we prove that if E(⎰dθ\2π│(C+e^(iθ) C-e^(iθ)_(kℓ)│^p)≤ C_(le)^kl∣k-ℓ∣ for some k_l > 0 and p < 1, then for suitable C_2 and k_2 > 0, E(sup_n∣(C^n)_kℓ∣) ≤C_2e^(-k_2∣k-ℓ∣. Here C is the CMV matrix.

Item Type:

Article

Related URLs:

URL	URL Type	Description
https://doi.org/10.1007/s00365-005-0599-4	DOI	Article
https://rdcu.be/uvN8	Publisher	Free ReadCube access
https://arxiv.org/abs/math/0411388	arXiv	Discussion Paper

ORCID:

Author	ORCID
Simon, Barry	0000-0003-2561-8539

Additional Information:

© Springer 2005. Date received: September 27, 2004. Date accepted: February 8, 2005. Online publication: June 3, 2005. Communicated by Percy A. Deift. Supported in part by NSF grant DMS-0140592. I would like to thank Mihai Stoiciu for useful discussions.

Funders:

Funding Agency	Grant Number
NSF	DMS-0140592

Subject Keywords:

OPUC, Random Verblunsky coefficients, Localization

Issue or Number:

Classification Code:

AMS classification: 26C05, 82B44, 47N20

DOI:

10.1007/s00365-005-0599-4

Record Number:

CaltechAUTHORS:20170726-134636444

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20170726-134636444

Official Citation:

Simon, B. Constr Approx (2006) 23: 229. https://doi.org/10.1007/s00365-005-0599-4

Usage Policy:

No commercial reproduction, distribution, display or performance rights in this work are provided.

ID Code:

79429

Collection:

CaltechAUTHORS

Deposited By:

Ruth Sustaita

Deposited On:

26 Jul 2017 21:58

Last Modified:

15 Nov 2021 17:48

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