Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral statistics for ensembles of various real random matrices   We investigate spacing statistics $p(s)$ and distribution of eigenvalues
$D(\epsilon)$ for ensembles of various real random matrices (of order $n \times
n, n=2$ and $n>>2$) where the matrix-elements have various Probability
Distribution Function (PDF: $f(x)$) including Gaussian. We construct ensembles
of $1000$, $100 \times 100$ real random matrices $R$, $C$ (cyclic) and $T$
(tridiagonal) and real symmetric matrices: ${\cal R}'$, ${\cal R}=R+R^t$,
${\cal Q}=RR^t$, ${\cal C}$ (cyclic), ${\cal T}$ (tridiagonal), $T'$
(pseudo-symmetric Tridiagonal), $\Theta$ (Toeplitz) , ${\cal D}=CC^t$ and
${\cal S}=TT^t$. We find that the spacing distribution of the adjacent levels
of matrices ${\cal R}$ and ${\cal R}'$ under any symmetric PDF of matrix
elements is $p_{AB}(s)=A s e^{-Bs^2}$ which approximately conforms to the
Wigner surmise as $A/2 \approx B \approx \pi/4$. But under asymmetric PDFs we
observe $A/2 \approx B >>\pi/4$, where $A,B$ are also sensitive to the choice
of the matrix and the PDF. More interestingly, the real symmetric matrices
${\cal C}, {\cal T}, {\cal Q}$, $\Theta$ (excepting ${\cal D}$ and ${\cal S}$)
and $T'$ (pseudo-symmetric tridiagonal) all conform to the Poisson distribution
$p_{\mu}(s) =\mu e^{-\mu s}$, where $\mu$ depends upon the choice of the matrix
and PDF. Let complex eigenvalues of $R$, $C$ and $T$ be $E^c_n$. We show that
all $p(s)$ arising due to $\Re(E^c_n)$, $\Im(E^c_n)$ and $|E^c_n|$ of $R$, $C$
and $T$ are also of Poisson type: $\mu e^{-\mu s}$. We observe $p(s)$ as
half-Gaussian for two real eigenvalues of $C$. For real matrices $R, C, T$, we
associate new types of $p(s)$ with them. Lastly, we study the distribution
$D(\epsilon)$ of eigenvalues of symmetric matrices (of large order) discussed
above.

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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat