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SOME REMARKS ON THE ELLIPTIC HARNACK INEQUALITY

Published online by Cambridge University Press:  10 March 2005

MARTIN T. BARLOW
MARTIN T. BARLOW
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2, Canada
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Abstract

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 inequality for Green's functions. The third result uses the lamplighter group to give a counter-example concerning the relation of coupling with the elliptic Harnack inequality

Keywords

31B05 (primary)60J3531C25 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 2 , March 2005 , pp. 200 - 208
Copyright
© The London Mathematical Society 2005

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Footnotes

Research partially supported by grants from NSERC (Canada) and CNRS (France).