Published January 2006 | Version Submitted
Journal Article Open

Aizenman's Theorem for Orthogonal Polynomials on the Unit Circle

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.

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.

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Additional details

Identifiers

Eprint ID
79429
DOI
10.1007/s00365-005-0599-4
Resolver ID
CaltechAUTHORS:20170726-134636444

Related works

Funding

NSF
DMS-0140592

Dates

Created
2017-07-26
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Updated
2021-11-15
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