Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The logarithmic law of random determinant   Consider the square random matrix $A_n=(a_{ij})_{n,n}$, where
$\{a_{ij}:=a_{ij}^{(n)},i,j=1,\ldots,n\}$ is a collection of independent real
random variables with means zero and variances one. Under the additional moment
condition \[\sup_n\max_{1\leq i,j\leq n}\mathbb{E}a_{ij}^4<\infty,\] we prove
Girko's logarithmic law of $\det A_n$ in the sense that as $n\rightarrow\infty$
\begin{eqnarray*}\frac{\log|\det A_n|-(1/2)\log(n-1)!}{\sqrt{(1/2)\log
n}}\stackrel{d}{ \longrightarrow}N(0,1).\end{eqnarray*}

8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga