Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on multi-dimensional noncommutative generalized Brownian motions   We consider certain questions pertaining to noncommutative generalized
Brownian motions with multiple processes. We establish a framework for
generalized Brownian motion with multiple processes similar to that defined by
Guta and prove multi-dimensional analogs of some results of Guta and Maassen.
We then consider examples of processes indexed by a two-element set and
characterize the function on I-indexed pair partitions associated via the
I-indexed generalized Brownian motion construction to certain pairs of
representations connected to certain spherical representations of infinite
symmetric groups. In doing so, we generalize the notion (introduced by Bozejko
and Guta) of the cycle decomposition of a pair partition. We then generalize
Guta's q-product of generalized Brownian motions to a product corresponding to
a (possibly infinite) matrix $(q_{ij})$ and show that this $q_{ij}$-product
satisfies a central limit theorem.

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The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th