Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the operator-valued analogues of the semicircle, arcsine and
  Bernoulli laws   We study of the connection between operator valued central limits for
monotone, Boolean and free probability theory, which we shall call the arcsine,
Bernoulli and semicircle distributions, respectively. In scalar-valued
non-commutative probability these measures are known to satisfy certain
arithmetic relations with respect to Boolean and free convolutions. We show
that generally the corresponding operator-valued distributions satisfy the same
relations only when we consider them in the fully matricial sense introduced by
Voiculescu. In addition, we provide a combinatorial description in terms of
moments of the operator valued arcsine distribution and we show that its
reciprocal Cauchy transform satisfies a version of the Abel equation similar to
the one satisfied in the scalar-valued case.

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The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
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The categories of this paper are: eess
4
The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org