# Note on short time behavior of semigroups associated to selfadjoint operators

#### Autoren: Matthias Keller, Daniel Lenz, Florentin Münch, Marcel Schmidt, Andras Telcs (2016)

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.

Zeitschrift:
Bullettin of the London Mathematical Society, to appear

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