Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limit distributions for large P\'{o}lya urns   We consider a two-color P\'{o}lya urn in the case when a fixed number $S$ of
balls is added at each step. Assume it is a large urn that is, the second
eigenvalue $m$ of the replacement matrix satisfies $1/2<m/S\leq1$. After $n$
drawings, the composition vector has asymptotically a first deterministic term
of order $n$ and a second random term of order $n^{m/S}$. The object of
interest is the limit distribution of this random term. The method consists in
embedding the discrete-time urn in continuous time, getting a two-type
branching process. The dislocation equations associated with this process lead
to a system of two differential equations satisfied by the Fourier transforms
of the limit distributions. The resolution is carried out and it turns out that
the Fourier transforms are explicitly related to Abelian integrals over the
Fermat curve of degree $m$. The limit laws appear to constitute a new family of
probability densities supported by the whole real line.

32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess