Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A noncommutative extended de Finetti theorem   The extended de Finetti theorem characterizes exchangeable infinite random
sequences as conditionally i.i.d. and shows that the apparently weaker
distributional symmetry of spreadability is equivalent to exchangeability. Our
main result is a noncommutative version of this theorem.
  In contrast to the classical result of Ryll-Nadzewski, exchangeability turns
out to be stronger than spreadability for infinite noncommutative random
sequences. Out of our investigations emerges noncommutative conditional
independence in terms of a von Neumann algebraic structure closely related to
Popa's notion of commuting squares and K\"ummerer's generalized Bernoulli
shifts. Our main result is applicable to classical probability, quantum
probability, in particular free probability, braid group representations and
Jones subfactors.

20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat