Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: What is a stochastic Hamiltonian process on finite graph? An optimal
  transport answer   We present a definition of stochastic Hamiltonian process on finite graph via
its corresponding density dynamics in Wasserstein manifold. We demonstrate the
existence of stochastic Hamiltonian process in many classical discrete
problems, such as the optimal transport problem, Schr\"odinger equation and
Schr\"odinger bridge problem (SBP). The stationary and periodic properties of
Hamiltonian processes are also investigated in the framework of SBP.

1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc