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HEAT KERNEL ESTIMATES ON WEIGHTED GRAPHS

Published online by Cambridge University Press:  01 July 2000

BERND METZGER  and
PETER STOLLMANN
BERND METZGER
Affiliation:
Fachbereich Mathematik, Universität Frankfurt, D-60054 Frankfurt, Germany
PETER STOLLMANN
Affiliation:
Fachbereich Mathematik, Universität Frankfurt, D-60054 Frankfurt, Germany
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Abstract

We prove upper and lower heat kernel bounds for the Laplacian on weighted graphs which include the case that the weights have no strictly positive lower bound. Our estimates give rise to a very explicit probabilistic interpretation, and can be formulated in terms of a weighted metric. Interestingly, this metric is not equivalent to the intrinsic metric.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 4 , July 2000 , pp. 477 - 483
Copyright
© The London Mathematical Society 2000

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