Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact Largest Eigenvalue Distribution for Doubly Singular Beta Ensemble   In \cite{Diaz} beta type I and II doubly singular distributions were
introduced and their densities and the joint densities of nonzero eigenvalues
were derived. In such matrix variate distributions $p$, the dimension of two
singular Wishart distributions defining beta distribution is larger than $m$
and $q$, degrees of freedom of Wishart matrices. We found simple formula to
compute exact largest eigenvalue distribution for doubly singular beta ensemble
in case of identity scale matrix, $\Sigma=I$. Distribution is presented in
terms of existing expression for CDF of Roy's statistic: $\lambda_{max} \sim
max \ eig\left\{ W_q(m, I)W_q(p-m+q, I)^{-1}\right\}$, where $W_k(n, I)$ is
Wishart distribution with $k$ dimensions, $n$ degrees of freedom and identity
scale matrix.

17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
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The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: eess
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc