Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Aizenman's Theorem for Orthogonal Polynomials on the Unit Circle   For suitable classes of random Verblunsky coefficients, including
independent, identically distributed, rotationally invariant ones, we prove
that if \[ \mathbb{E} \biggl(\int\frac{d\theta}{2\pi}
\biggl|\biggl(\frac{\mathcal{C} + e^{i\theta}}{\mathcal{C} -e^{i\theta}}
\biggr)_{k\ell}\biggr|^p \biggr) \leq C_1 e^{-\kappa_1 |k-\ell|} \] for some
$\kappa_1 >0$ and $p<1$, then for suitable $C_2$ and $\kappa_2 >0$, \[
\mathbb{E} \bigl(\sup_n |(\mathcal{C}^n)_{k\ell}|\bigr) \leq C_2 e^{-\kappa_2
|k-\ell|} \] Here $\mathcal{C}$ is the CMV matrix.

21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs