Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free infinite divisibility for beta distributions and related ones   We prove that many of beta, beta prime, gamma, inverse gamma, Student t- and
ultraspherical distributions are freely infinitely divisible, but some of them
are not. The latter negative result follows from a local property of
probability density functions. Moreover, we show that the Gaussian,
ultraspherical and many of Student t-distributions have free divisibility
indicator 1.

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The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
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The categories of this paper are: econ
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph