Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Evaluating moments of length of Pitman partition   The Pitman sampling formula has been intensively studied as a distribution of
random partitions. One of the objects of interest is the length $K (=
K_{n,\theta,\alpha})$ of a random partition that follows the Pitman sampling
formula, where $n\in\mathbb{N}$, $\alpha\in(0,\infty)$ and $\theta > -\alpha$
are parameters. This paper presents asymptotic evaluations of its $r$-th moment
$\mathsf{E}[K^r]$ ($r=1,2,\ldots$) under two asymptotic regimes. In particular,
the goals of this study are to provide a finer approximate evaluation of
$\mathsf{E}[K^r]$ as $n\to\infty$ than has previously been developed and to
provide an approximate evaluation of $\mathsf{E}[K^r]$ as the parameters $n$
and $\theta$ simultaneously tend to infinity with $\theta/n \to 0$. The results
presented in this paper will provide a more accurate understanding of the
asymptotic behavior of $K$.

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The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
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The categories of this paper are: eess
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
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The categories of this paper are: econ
27
The categories of this paper are: comp-gas