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Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters

Abstract:
We consider the random walk on supercritical percolation clusters in ℤd. Previous papers have obtained Gaussian heat kernel bounds, and a.s. invariance principles for this process. We show how this information leads to a parabolic Harnack inequality, a local limit theorem and estimates on the Green's function.
Publication status:
Published

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
ELECTRONIC JOURNAL OF PROBABILITY More from this journal
Volume:
14
Pages:
1-26
Publication date:
2009-01-07
EISSN:
1083-6489
ISSN:
1083-6489
Language:
English
Keywords:
Pubs id:
pubs:376
UUID:
uuid:2217ddea-aa91-4e2a-ace7-143a004f0f32
Local pid:
pubs:376
Source identifiers:
376
Deposit date:
2012-12-19

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