Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moments of the frequency spectrum of a splitting tree with neutral
  Poissonian mutations   We consider a branching population where individuals live and reproduce
independently. Their lifetimes are i.i.d. and they give birth at a constant
rate b. The genealogical tree spanned by this process is called a splitting
tree, and the population counting process is a homogeneous, binary
Crump-Mode-Jagers process. We suppose that mutations affect individuals
independently at a constant rate $\\theta$ during their lifetimes, under the
infinite-alleles assumption: each new mutation gives a new type, called allele,
to his carrier. We study the allele frequency spectrum which is the numbers
A(k, t) of types represented by k alive individuals in the population at time
t. Thanks to a new construction of the coalescent point process describing the
genealogy of individuals in the splitting tree, we are able to compute
recursively all joint factorial moments of (A(k, t)) k$\ge$1. These moments
allow us to give an elementary proof of the almost sure convergence of the
frequency spectrum in a supercritical splitting tree.

37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc