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Aizenman's Theorem for Orthogonal Polynomials on the Unit Circle | | Barry Simon
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17 Nov 2004 | | Subject: | Spectral Theory MSC-class: 26C05, 82B44, 47N20 | math.SP | | Abstract: | For suitable classes of random Verblunsky coefficients, including independent, identically distributed, rotationally invariant ones, we prove that if mathbb{E} iggl(intfrac{d heta}{2pi} iggl|iggl(frac{mathcal{C} + e^{i heta}}{mathcal{C} -e^{i heta}} iggr)_{kell}iggr|^p iggr) leq C_1 e^{-kappa_1 |k-ell|} for some $kappa_1 >0$ and $p<1$, then for suitable $C_2$ and $kappa_2 >0$, mathbb{E} igl(sup_n |(mathcal{C}^n)_{kell}|igr) leq C_2 e^{-kappa_2 |k-ell|} Here $mathcal{C}$ is the CMV matrix. | | Source: | arXiv, math.SP/0411388 | | Services: | Forum | Review | PDF | Favorites | |
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