Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Four Deviations Suffice for Rank 1 Matrices   We prove a matrix discrepancy bound that strengthens the famous
Kadison-Singer result of Marcus, Spielman, and Srivastava. Consider any
independent scalar random variables $\xi_1, \ldots, \xi_n$ with finite support,
e.g.
  $\{ \pm 1 \}$ or $\{ 0,1 \}$-valued random variables, or some combination
thereof. Let $u_1, \dots, u_n \in \mathbb{C}^m$ and $$ \sigma^2 = \left\|
\sum_{i=1}^n \text{Var}[ \xi_i ] (u_i u_i^{*})^2 \right\|. $$ Then there exists
a choice of outcomes $\varepsilon_1,\ldots,\varepsilon_n$ in the support of
$\xi_1, \ldots, \xi_n$ s.t. $$ \left \|\sum_{i=1}^n \mathbb{E} [ \xi_i] u_i
u_i^* - \sum_{i=1}^n \varepsilon_i u_i u_i^* \right \| \leq 4 \sigma. $$ A
simple consequence of our result is an improvement of a Lyapunov-type theorem
of Akemann and Weaver.

16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn