Publication Date:
2016-12-30
Description:
We present a simple observation showing that the heat kernel on a locally finite graph behaves for short times $t$ roughly like $t^d$ , where $d$ is the combinatorial distance. This is very different from the classical Varadhan-type behavior on manifolds. Moreover, this also gives that short-time behavior and global behavior of the heat kernel are governed by two different metrics whenever the degree of the graph is not uniformly bounded.
Print ISSN:
0024-6093
Electronic ISSN:
1469-2120
Topics:
Mathematics