Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Obtaining the long-term behavior of Master equations with finite state
  space from the structure of the associated state transition network   The Master equation describes the time evolution of the probabilities of a
system with a discrete state space. This time evolution approaches for long
times a stationary state that will in general depend on the initial probability
distribution. Conditions under which the stationary state is unique are usually
given as remarks appended to more comprehensive theories in the mathematical
literature. We provide a direct and complete derivation of a necessary and
sufficient criterion for when this steady state is unique. We translate this
problem into the language of graph theory and show that there is a one-to-one
correspondence between minimal absorbing sets within the state-transition
network and linearly independent stationary states of the Master equation.

28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ