Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poisson--Dirichlet Limit Theorems in Combinatorial Applications via
  Multi-Intensities   We present new, exceptionally efficient proofs of Poisson--Dirichlet limit
theorems for the scaled sizes of irreducible components of random elements in
the classic combinatorial contexts of arbitrary assemblies, multisets, and
selections, when the components generating functions satisfy certain standard
hypotheses. The proofs exploit a new criterion for Poisson--Dirichlet limits,
originally designed for rapid proofs of Billingsley's theorem on the scaled
sizes of log prime factors of random integers (and some new generalizations).
  Unexpectedly, the technique applies in the present combinatorial setting as
well, giving, perhaps, a long sought-after unifying point of view. The proofs
depend also on formulas of Arratia and Tavar{\'e} for the mixed moments of
counts of components of various sizes, as well as formulas of Flajolet and
Soria for the asymptotics of generating function coefficients.

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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex