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Gaussian Upper Bounds for Heat Kernels of Continuous Time Simple Random Walks


 
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1. Title Title of document Gaussian Upper Bounds for Heat Kernels of Continuous Time Simple Random Walks
 
2. Creator Author's name, affiliation, country Matthew Folz; University of British Columbia; Canada
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) random walk; heat kernel; Gaussian upper bound; random walk in random environment
 
3. Subject Subject classification 60G50; 30K08; 60K37
 
4. Description Abstract We consider continuous time simple random walks with arbitrary speed measure $\theta$ on infinite weighted graphs. Write $p_t(x,y)$ for the heat kernel of this process. Given on-diagonal upper bounds for the heat kernel at two points $x_1,x_2$, we obtain a Gaussian upper bound for $p_t(x_1,x_2)$. The distance function which appears in this estimate is not in general the graph metric, but a new metric which is adapted to the random walk. Long-range non-Gaussian bounds in this new metric are also established. Applications to heat kernel bounds for various models of random walks in random environments are discussed.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSERC
 
7. Date (YYYY-MM-DD) 2011-09-12
 
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/926
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-926
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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