Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A concentration inequality and a local law for the sum of two random
  matrices   Let H=A+UBU* where A and B are two N-by-N Hermitian matrices and U is a
Haar-distributed random unitary matrix, and let \mu_H, \mu_A, and \mu_B be
empirical measures of eigenvalues of matrices H, A, and B, respectively. Then,
it is known (see, for example, Pastur-Vasilchuk, CMP, 2000, v.214, pp.249-286)
that for large N, measure \mu_H is close to the free convolution of measures
\mu_A and \mu_B, where the free convolution is a non-linear operation on
probability measures.
  The large deviations of the cumulative distribution function of \mu_H from
its expectation have been studied by Chatterjee in in JFA, 2007, v. 245,
pp.379-389. In this paper we improve Chatterjee's concentration inequality and
show that it holds with the rate which is quadratic in N.
  In addition, we prove a local law for eigenvalues of H, by showing that the
normalized number of eigenvalues in an interval converges to the density of the
free convolution of \mu_A and \mu_B provided that the interval has width (log
N)^{-1/2}.

7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph