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The Beurling Estimate for a Class of Random Walks


 
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1. Title Title of document The Beurling Estimate for a Class of Random Walks
 
2. Creator Author's name, affiliation, country Gregory F Lawler; Cornell University
 
2. Creator Author's name, affiliation, country Vlada Limic; University of British Columbia
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Beurling projection; random walk; Green's function; escape probabilities
 
3. Subject Subject classification 60G50; 60F99
 
4. Description Abstract An estimate of Beurling states that if $K$ is a curve from $0$ to the unit circle in the complex plane, then the probability that a Brownian motion starting at $-\varepsilon$ reaches the unit circle without hitting the curve is bounded above by $c \varepsilon^{1/2}$. This estimate is very useful in analysis of boundary behavior of conformal maps, especially for connected but rough boundaries. The corresponding estimate for simple random walk was first proved by Kesten. In this note we extend this estimate to random walks with zero mean, finite $(3+\delta)$-moment.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) National Science Foundation and NSERC
 
7. Date (YYYY-MM-DD) 2004-12-13
 
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/228
 
10. Identifier Digital Object Identifier 10.1214/EJP.v9-228
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 9
 
12. Language English=en
 
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