Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The volume and time comparison principle and transition probability
  estimates for random walks   This paper presents necessary and sufficient conditions for on- and
off-diagonal transition probability estimates for random walks on weighted
graphs. On the integer lattice and on may fractal type graphs both the volume
of a ball and the mean exit time from a ball is independent of the centre,
uniform in space. Here the upper estimate is given without such restriction and
two-sided estimate is given if uniformity in the space assumed only for the
mean exit time.

21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an