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Parabolic Harnack inequality and local limit theorem for percolation clusters


 
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1. Title Title of document Parabolic Harnack inequality and local limit theorem for percolation clusters
 
2. Creator Author's name, affiliation, country Ben M Hambly; University of Oxford
 
2. Creator Author's name, affiliation, country Martin T Barlow; University of British Columbia
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Percolation; random walk; Harnack inequality; local limit theorem
 
3. Subject Subject classification 60G50; 31B05
 
4. Description Abstract We consider the random walk on supercritical percolation clusters in $\mathbb{Z}^d$. 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) UK EPSRC
 
7. Date (YYYY-MM-DD) 2009-01-07
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/587
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-587
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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