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SOME REMARKS ON THE ELLIPTIC HARNACK INEQUALITY

SOME REMARKS ON THE ELLIPTIC HARNACK INEQUALITY

Three short results are given concerning the elliptic Harnack inequality, in the context of random walks on graphs. The first is that the elliptic Harnack inequality implies polynomial growth of the number of points in balls, and the second that the elliptic Harnack inequality is equivalent to an annulus-type Harnack …