Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probability distributions with rational free $R$-transform   We study the class $\mathcal{M}_{\mathrm{ratio}}$ of those probability
distributions for which the free $R$-transforms are rational functions. This
class is closed under the additive free convolution, additive free powers and
under the monotone convolution. We prove a sufficient condition that a rational
function is the free $R$-transform of a probability distribution. Several
examples are provided, including that of free deconvolution.

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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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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
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex