Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coagulation Fragmentation Laws Induced By General Coagulations of
  Two-Parameter Poisson-Dirichlet Processes   Pitman~(1999) describes a duality relationship between fragmentation and
coagulation operators. An explicit relationship is described for the
two-parameter Poisson-Dirichlet laws, with parameters {\footnotesize
$(\alpha,\theta)$} and $(\beta,\theta/\alpha)$, wherein $PD(\alpha, \theta)$ is
coagulated by $PD(\beta,\theta/\alpha)$ for $0<\alpha<1$, $0 \leq\beta<1$ and
$-\beta<\theta/\alpha$. This remarkable explicit agreement was obtained by
combinatorial methods via exchangeable partition probability functions~(EPPF).
This work discusses an alternative analysis which can feasibly extend the
characterizations above to more general models of $PD(\alpha,\theta)$
coagulated with some law $Q$. The analysis exploits distributional
relationships between compositions of species sampling random probability
measures and coagulation operators and recent work on Cauchy-Stieltjes
transforms of random probability measures by Vershik, Yor and Tsilevich (2004)
and James (2002). We use this to obtain explicit descriptions in the case where
{\footnotesize $Q$} corresponds to a large class of power tempered Poisson
Kingman models analyzed in James~(2002). That is, explicit results are obtained
for models outside of the $PD(\beta,\theta/\alpha)$ family.

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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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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: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-th