Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gaussian upper bounds for heat kernels of continuous time simple random
  walks   We consider continuous time simple random walks with arbitrary speed measure
$\theta$ on infinite weighted graphs. Write $p_t(x,y)$ for the heat kernel of
this process. Given on-diagonal upper bounds for the heat kernel at two points
$x_1,x_2$, we obtain a Gaussian upper bound for $p_t(x_1,x_2)$. The distance
function which appears in this estimate is not in general the graph metric, but
a new metric which is adapted to the random walk. Long-range non-Gaussian
bounds in this new metric are also established. Applications to heat kernel
bounds for various models of random walks in random environments are discussed.

24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph