Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Restricted Isometry Property of Subsampled Fourier Matrices   A matrix $A \in \mathbb{C}^{q \times N}$ satisfies the restricted isometry
property of order $k$ with constant $\varepsilon$ if it preserves the $\ell_2$
norm of all $k$-sparse vectors up to a factor of $1\pm \varepsilon$. We prove
that a matrix $A$ obtained by randomly sampling $q = O(k \cdot \log^2 k \cdot
\log N)$ rows from an $N \times N$ Fourier matrix satisfies the restricted
isometry property of order $k$ with a fixed $\varepsilon$ with high
probability. This improves on Rudelson and Vershynin (Comm. Pure Appl. Math.,
2008), its subsequent improvements, and Bourgain (GAFA Seminar Notes, 2014).

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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: econ