Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The variance of the average depth of a pure birth process converges to 7   If trees are constructed from a pure birth process and one defines the depth
of a leaf to be the number of edges to its root, it is known that the variance
in the depth of a randomly selected leaf of a randomly selected tree grows
linearly in time. In this letter, we instead consider the variance of the
average depth of leaves within each individual tree, establishing that, in
contrast, it converges to a constant, $7$. This result indicates that while the
variance in leaf depths amongst the ensemble of pure birth processes undergoes
large fluctuations, the average depth across individual trees is much more
consistent.

18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th