Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Partitioning Problems Involving Poisson Point Processes On The
  Interval   Suppose some random resource (energy, mass or space) $\chi \geq 0$ is to be
shared at random between (possibly infinitely many) species (atoms or
fragments). Assume ${\Bbb E}\chi =\theta <\infty $ and suppose the amount of
the individual share is necessarily bounded from above by 1. This random
partitioning model can naturally be identified with the study of infinitely
divisible random variables with L\'{e}vy measure concentrated on the interval%
$.$ Special emphasis is put on these special partitioning models in the
Poisson-Kingman class. The masses attached to the atoms of such partitions are
sorted in decreasing order. Considering nearest- neighbors spacings yields a
partition of unity which also deserves special interest. For such partition
models, various statistical questions are addressed among which: correlation
structure, cumulative energy of the first $K$ largest items, partition
function, threshold and covering statistics, weighted partition, R\'{e}nyi's,
typical and size-biased fragments size. Several physical images are supplied.
When the unbounded L\'{e}vy measure of $\chi $ is $\theta x^{-1}\cdot {\bf I}%
(x\in (0,1)) dx$, the spacings partition has Griffiths-Engen-McCloskey or
GEM$(\theta) $ distribution and $% \chi $ follows Dickman distribution. The
induced partition models have many remarkable peculiarities which are outlined.
The case with finitely many (Poisson) fragments in the partition law is also
briefly addressed. Here, the L\'{e}vy measure is bounded.

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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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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: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an