Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The first Dirichlet eigenvalue of birth-death process on tree   This paper investigates the birth-death ("B-D" for short) process on tree
with continuous time, emphasizing on estimating the principal eigenvalue
(equivalently, the convergence rate) of the process with Dirichlet boundary at
the unique root 0. Three kinds of variational formulas for the eigenvalue are
presented. As an application, we obtain a criterion for positivity of the first
eigenvalue for B-D processes on tree with one branch after some layer.

3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int