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Convergence of Lattice Trees to Super-Brownian Motion above the Critical Dimension


 
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1. Title Title of document Convergence of Lattice Trees to Super-Brownian Motion above the Critical Dimension
 
2. Creator Author's name, affiliation, country Mark P. Holmes; U. Auckland
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Lattice trees; super-Brownian motion; lace expansion.
 
3. Subject Subject classification 82B41; 60F05; 60G57; 60K35.
 
4. Description Abstract We use the lace expansion to prove asymptotic formulae for the Fourier transforms of the $r$-point functions for a spread-out model of critically weighted lattice trees on the $d$-dimensional integer lattice for $d > 8$. A lattice tree containing the origin defines a sequence of measures on the lattice, and the statistical mechanics literature gives rise to a natural probability measure on the collection of such lattice trees. Under this probability measure, our results, together with the appropriate limiting behaviour for the survival probability, imply convergence to super-Brownian excursion in the sense of finite-dimensional distributions.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2008-04-18
 
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/499
 
10. Identifier Digital Object Identifier 10.1214/EJP.v13-499
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 13
 
12. Language English=en
 
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