Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multivariate reciprocal inverse Gaussian distributions from the Sabot
  -Tarr\`es -Zeng integral   In Sabot and Tarr\`es (2015), the authors have explicitly computed the
integral $$STZ_n=\int \exp( -\langle x,y\rangle)(\det M_x)^{-1/2}dx$$ where
$M_x$ is a symmetric matrix of order $n$ with fixed non positive off-diagonal
coefficients and with diagonal $(2x_1,\ldots,2x_n)$. The domain of integration
is the part of $\mathbb{R}^n$ for which $M_x$ is positive definite. We
calculate more generally for $ b_1\geq 0,\ldots b_n\geq 0$ the integral
$$GSTZ_n=\int \exp \left(-\langle
x,y\rangle-\frac{1}{2}b^*M_x^{-1}b\right)(\det M_x)^{-1/2}dx,$$ we show that it
leads to a natural family of distributions in $\mathbb{R}^n$, called the
$GSTZ_n$ probability laws. This family is stable by marginalization and by
conditioning, and it has number of properties which are multivariate versions
of familiar properties of univariate reciprocal inverse Gaussian distribution.
We also show that if the graph with the set of vertices $V=\{1,\ldots,n\}$ and
the set $E$ of edges $\{i,j\}'$ s of non zero entries of $M_x$ is a tree, then
the integral $$\int \exp( -\langle x,y\rangle)(\det M_x)^{q-1}dx$$ where $q>0,$
is computable in terms of the MacDonald function $K_q.$

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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph