Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two dimensional Meixner random vectors of class ${\mathcal M}_L$   The paper is divided into two parts. In the first part we lay down the
foundation for defining the joint annihilation-preservation-creation
decomposition of a finite family of, not necessarily commutative random
variables, and show that this decomposition is essentially unique. In the
second part we show that any two, not necessarily commutative, random variables
$X$ and $Y$, for which the vector space spanned by their annihilation,
preservation, and creation operators equipped with the bracket given by the
commutator, forms a Lie algebra, are equivalent, up to an invertible linear
transformation to two independent Meixner random variables with mixed
preservation operators. In particular if $X$ and $Y$ commute, then they are
equivalent, up to an invertible linear transformation to two independent
classic Meixner random variables. To show this we start with a small technical
condition called "non-degeneracy".

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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat