Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Traffic Distributions and Independence II: Universal Constructions for
  Traffic Spaces   We investigate questions related to the notion of traffics introduced by the
author C. Male as a noncommutative probability space with numerous additional
operations and equipped with the notion of traffic independence. We prove that
any sequence of unitarily invariant random matrices that converges in
noncommutative distribution converges in distribution of traffics whenever it
fulfills some factorization property. We provide an explicit description of the
limit which allows to recover and extend some applications (on the freeness
from the transposed ensembles by Mingo and Popa and the freeness of infinite
transitive graphs by Accardi, Lenczewski and Salapata). We also improve the
theory of traffic spaces by considering a positivity axiom related to the
notion of state in noncommutative probability. We construct the free product of
spaces of traffics and prove that it preserves the positivity condition. This
analysis leads to our main result stating that every noncommutative probability
space endowed with a tracial state can be enlarged and equipped with a
structure of space of traffics.

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The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th