Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The coalescent point process of branching trees   We define a doubly infinite, monotone labeling of Bienayme-Galton-Watson
(BGW) genealogies. The genealogy of the current generation backwards in time is
uniquely determined by the coalescent point process $(A_i; i\ge 1)$, where
$A_i$ is the coalescence time between individuals i and i+1. There is a Markov
process of point measures $(B_i; i\ge 1)$ keeping track of more ancestral
relationships, such that $A_i$ is also the first point mass of $B_i$. This
process of point measures is also closely related to an inhomogeneous spine
decomposition of the lineage of the first surviving particle in generation h in
a planar BGW tree conditioned to survive h generations. The decomposition
involves a point measure $\rho$ storing the number of subtrees on the
right-hand side of the spine. Under appropriate conditions, we prove
convergence of this point measure to a point measure on $\mathbb{R}_+$
associated with the limiting continuous-state branching (CSB) process. We prove
the associated invariance principle for the coalescent point process, after we
discretize the limiting CSB population by considering only points with
coalescence times greater than $\varepsilon$.

18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th