Some remarks on the elliptic Harnack inequality

Details Some remarks on the elliptic Harnack inequality Some remarks on the elliptic Harnack inequality

2003-09-02

arxiv.org/abs/math/0309052v1

Mathematics

Probability

Scientific paper

This note gives three short results concerning the elliptic Harnack inequality (EHI), in the context of random walks on graphs. The first is that the EHI implies polynomial growth of the number of points in balls, and the second that the EHI is equivalent to an annulus type Harnack inequality for Green's functions. The third result uses the lamplighter group to give a counterexample concerning the relation of coupling with the EHI.

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