Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential bounds for the support convergence in the Single Ring
  Theorem   We consider an $n$ by $n$ matrix of the form $A=UTV$, with $U, V$ some
independent Haar-distributed unitary matrices and $T$ a deterministic matrix.
We prove that for $k\sim n^{1/6}$ and
$b^2:=\frac{1}{n}\operatorname{Tr}(|T|^2)$, as $n$ tends to infinity, we have
$$\mathbb{E} \operatorname{Tr} (A^{k}(A^{k})^*) \ \lesssim \ b^{2k}\qquad
\textrm{and} \qquad\mathbb{E}[|\operatorname{Tr} (A^{k})|^2] \ \lesssim \
b^{2k}.$$ This gives a simple proof (with slightly weakened hypothesis) of the
convergence of the support in the Single Ring Theorem, improves the available
error bound for this convergence from $n^{-\alpha}$ to $e^{-cn^{1/6}}$ and
proves that the rate of this convergence is at most $n^{-1/6}\log n$.

1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph