Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Characterization of Freeness by a Factorization Property of
  R-transform   Let M be a B-probability space. Assume that B itself is a D-probability
space; then M can be viewed as a D-probability space as well. Let X be in M. We
characterize freeness of X from B with amalgamation over D in terms of a
certain factorization condition linking the B-valued and D-valued R-transforms
of X. We give an application to random matrices.

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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin