Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A universal expectation bound on empirical projections of deformed
  random matrices   Let $C$ be a real-valued $M\times M$ matrix with singular values
$\lambda_1\ge...\ge\lambda_M$ and $E$ a random matrix of centered i.i.d.
entries with finite fourth moment. In this paper we give a universal upper
bound on the expectation of $||\hat\pi_rX||_{S_2}^2-||\pi_rX||^2_{S_2}$, where
$X:=C+E$ and $\hat\pi_r$ (resp. $\pi_r$) is a rank-$r$ projection maximizing
the Hilbert-Schmidt norm $||\tilde\pi_rX||_{S_2}$ (resp.
$||\tilde\pi_rC||_{S_2}$) over the set $\S_{M,r}$ of all orthogonal rank-$r$
projections. This result is a generalization of a theorem for Gaussian matrices
due to Rohde (2012). Our approach differs substantially from the techniques of
the mentioned article. We analyze $||\hat\pi_rX||_{S_2}^2-||\pi_rX||^2_{S_2}$
from a rather deterministic point of view by an upper bound on
$||\hat\pi_rX||_{S_2}^2-||\pi_rX||^2_{S_2}$, whose randomness is totally
determined by the largest singular value of $E$.

12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics