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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. 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:
URLURL TypeDescription
https://doi.org/10.1007/s00365-005-0599-4DOIArticle
https://rdcu.be/uvN8PublisherFree ReadCube access
https://arxiv.org/abs/math/0411388arXivDiscussion Paper
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
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 AgencyGrant Number
NSFDMS-0140592
Subject Keywords:OPUC, Random Verblunsky coefficients, Localization
Issue or Number:2
Classification Code:AMS classification: 26C05, 82B44, 47N20
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:31 Jan 2020 16:00

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