Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Addition of Free Unitary Random Matrices   We consider a new class of non-Hermitian random matrices, namely the ones
which have the form of sums of freely independent terms involving unitary
matrices. To deal with them, we exploit the recently developed quaternion
technique. After having derived some general identities describing additive
properties of unitary matrices, we solve three particular models: CUE plus CUE,
CUE plus... plus CUE (i. e. the sum of an arbitrary number of CUE matrices),
and CUE plus GUE. By solution of a given model we mean here to calculate the
borderline of the eigenvalues' two-dimensional domain, as well as the
eigenvalues' density function inside the domain. We confirm numerically all the
results, obtaining very good agreement.

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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph