Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Estimate on the Number of Eigenvalues of a Quasiperiodic Jacobi
  Matrix of Size $n$ Contained in an Interval of Size $n^{-C}$   We consider infinite quasi-periodic Jacobi self-adjoint matrices for which
the three main diagonals are given via values of real analytic functions on the
trajectory of the shift $x\rightarrow x+\omega$. We assume that the Lyapunov
exponent $L(E_{0})$ of the corresponding Jacobi cocycle satisfies
$L(E_{0})\ge\gamma>0$. In this setting we prove that the number of eigenvalues
$E_{j}^{(n)}(x)$ of a submatrix of size $n$ contained in an interval $I$
centered at $E_{0}$ with $|I|=n^{-C_{1}}$ does not exceed $(\log n)^{C_{0}}$
for any $x$. Here $n\ge n_{0}$, and $n_{0}$, $C_{0}$, $C_{1}$ are constants
depending on $\gamma$ (and the other parameters of the problem).

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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org