Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some characterisation results on classical and free Poisson thinning   Poisson thinning is an elementary result in probability, which is of great
importance in the theory of Poisson point processes. In this article, we record
a couple of characterisation results on Poisson thinning. We also consider free
Poisson thinning, the free probability analogue of Poisson thinning, which
arises naturally as a high-dimensional asymptotic analogue of Cochran's theorem
from multivariate statistics on the "Wishart-ness" of quadratic functions of
Gaussian random matrices. The main difference between classical and free
Poisson thinning is that, in the former, the involved Poisson random variable
can have an arbitrary mean, whereas, in the free version, the "mean" of the
relevant free Poisson variable must be 1. We prove similar characterisation
results for free Poisson thinning and note their implications in the context of
Cochran's theorem.

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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio