Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Markov processes on time-like graphs   We study Markov processes where the "time" parameter is replaced by paths in
a directed graph from an initial vertex to a terminal one. Along each directed
path the process is Markov and has the same distribution as the one along any
other directed path. If two directed paths do not interact, in a suitable
sense, then the distributions of the processes on the two paths are
conditionally independent, given their values at the common endpoint of the two
paths. Conditions on graphs that support such processes (e.g., hexagonal
lattice) are established. Next we analyze a particularly suitable family of
Markov processes, called harnesses, which includes Brownian motion and other
L\'{e}vy processes, on such time-like graphs. Finally we investigate continuum
limits of harnesses on a sequence of time-like graphs that admits a limit in a
suitable sense.

1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th