Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second Order Cumulants: second order even elements and R-diagonal
  elements   We introduce $R$-diagonal and even operators of second order. We give a
formula for the second order free cumulants of the square $x^2$ of a second
order even element in terms of the second order free cumulants of $x$. Similar
formulas are proved for the second order free cumulants of $aa^*$, when $a$ is
a second order $R$-diagonal operator. We also show that if $r$ is second order
$R$-diagonal and $b$ is second order free from $r$, then $rb$ is also second
order $R$-diagonal. We present a large number of examples, in particular the
limit distribution of products of Ginibre matrices. We prove the conjectured
formula of Dartois and Forrester for the fluctuations moments of the product of
two independent complex Wishart matrices and generalize it to any number of
factors.

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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th