Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic completeness of graphs: bounded Laplacians, intrinsic
  metrics, volume growth and curvature   The goal of this article is to survey various results concerning stochastic
completeness of graphs. In particular, we present a variety of formulations of
stochastic completeness and discuss how a discrepancy between uniqueness class
and volume growth criteria in the continuous and discrete settings was
ultimately resolved via the use of intrinsic metrics. Along the way, we discuss
some equivalent notions of boundedness in the sense of geometry and of
analysis. We also discuss various curvature criteria for stochastic
completeness and discuss how weakly spherically symmetric graphs establish the
sharpness of results.

20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs