Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A combinatorial representation for the invariant measure of diffusion
  processes on metric graphs   We give a generalization to a continuous setting of the classic Markov chain
tree Theorem. In particular, we consider an irreducible diffusion process on a
metric graph. The unique invariant measure has an atomic component on the
vertices and an absolutely continuous part on the edges. We show that the
corresponding density at $x$ can be represented by a normalized superposition
of the weights associated to metric arborescences oriented toward the point
$x$. The weight of each oriented metric arborescence is obtained by the
exponential of integrals of the form $\int\frac{b}{\sigma^2}$ along the
oriented edges time a weight for each node determined by the local orientation
of the arborescence around the node time the inverse of the diffusion
coefficient at $x$. The metric arborescences are obtained cutting the original
metric graph along some edges.

3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph