Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Tracy-Widom law for the Largest Eigenvalue of F Type Matrix   Let $\mathbb{A}_p=\frac{\mathbb{Y}\mathbb{Y}^*}{m}$ and
$\mathbb{B}_p=\frac{\mathbb{X}\mathbb{X}^*}{n}$ be two independent random
matrices where $\mathbb{X}=(X_{ij})_{p \times n}$ and $\mathbb{Y}=(Y_{ij})_{p
\times m}$ respectively consist of real (or complex) independent random
variables with $\mathbb{E}X_{ij}=\mathbb{E}Y_{ij}=0$,
$\mathbb{E}|X_{ij}|^2=\mathbb{E}|Y_{ij}|^2=1$. Denote by $\lambda_{1}$ the
largest root of the determinantal equation $\det(\lambda
\mathbb{A}_p-\mathbb{B}_p)=0$. We establish the Tracy-Widom type universality
for $\lambda_{1}$ under some moment conditions on $X_{ij}$ and $Y_{ij}$ when
$p/m$ and $p/n$ approach positive constants as $p\rightarrow\infty$.

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The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph