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Functional CLT for Random Walk Among Bounded Random Conductances


 
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1. Title Title of document Functional CLT for Random Walk Among Bounded Random Conductances
 
2. Creator Author's name, affiliation, country Marek Biskup; UCLA
 
2. Creator Author's name, affiliation, country Timothy M Prescott; UCLA
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random conductance model, invariance principle, corrector, homogenization, heat kernel, percolation, isoperimetry
 
3. Subject Subject classification 60K37; 60F05; 82C41
 
4. Description Abstract We consider the nearest-neighbor simple random walk on $Z^d$, $d\ge2$, driven by a field of i.i.d. random nearest-neighbor conductances $\omega_{xy}\in[0,1]$. Apart from the requirement that the bonds with positive conductances percolate, we pose no restriction on the law of the $\omega$'s. We prove that, for a.e. realization of the environment, the path distribution of the walk converges weakly to that of non-degenerate, isotropic Brownian motion. The quenched functional CLT holds despite the fact that the local CLT may fail in $d\ge5$ due to anomalously slow decay of the probability that the walk returns to the starting point at a given time.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF grant DMS-0505356
 
7. Date (YYYY-MM-DD) 2007-10-25
 
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/456
 
10. Identifier Digital Object Identifier 10.1214/EJP.v12-456
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 12
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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