Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Family size decomposition of genealogical trees   We study the path of family size decompositions of varying depth of
genealogical trees. We prove that this decomposition as a function on
(equivalence classes of) ultra-metric measure spaces to the Skorohod space
describing the family sizes at different depths is perfect onto its image, i.e.
there is a suitable topology such that this map is continuous closed surjective
and pre-images of compact sets are compact. We also specify a (dense) subset so
that the restriction of the function to this subspace is a homeomorphism. This
property allows us to argue that the whole genealogy of a Fleming-Viot process
with mutation and selection as well as the genealogy in a Feller branching
population can be reconstructed by the genealogical distance of two randomly
chosen individuals.

27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga