Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Genealogies of regular exchangeable coalescents with applications to
  sampling   This article considers a model of genealogy corresponding to a regular
exchangeable coalescent (also known as Xi-coalescent) started from a large
finite configuration, and undergoing neutral mutations. Asymptotic expressions
for the number of active lineages were obtained by the author in a previous
work. Analogous results for the number of active mutation-free lineages and the
combined lineage lengths are derived using the same martingale-based technique.
They are given in terms of convergence in probability, while extensions to
convergence in moments and convergence almost surely are discussed. The above
mentioned results have direct consequences on the sampling theory in the
Xi-coalescent setting. In particular, the regular Xi-coalescents that come down
from infinity (i.e., with locally finite genealogies), have an asymptotically
equal number of families under the corresponding infinite alleles and infinite
sites models. In special cases, quantitative asymptotic formulae for the number
of families that contain a fixed number of individuals can be given.

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The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
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The categories of this paper are: q-fin
29
The categories of this paper are: funct-an