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The growth constants of lattice trees and lattice animals in high dimensions


 
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1. Title Title of document The growth constants of lattice trees and lattice animals in high dimensions
 
2. Creator Author's name, affiliation, country Yuri Mejia Miranda; University of British Columbia
 
2. Creator Author's name, affiliation, country Gordon Slade; University of British Columbia
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) growth constant; lattice tree; lattice animal; mean-field model
 
3. Subject Subject classification 60K35; 82B41
 
4. Description Abstract We prove that the growth constants for nearest-neighbour lattice trees and lattice (bond) animals on the integer lattice $\mathbb{Z}^d$ are asymptotic to $2de$ as the dimension goes to infinity, and that their critical one-point functions converge to $e$. Similar results are obtained in dimensions $d > 8$ in the limit of increasingly spread-out models; in this case the result for the growth constant is a special case of previous results of M. Penrose. The proof is elementary, once we apply previous results of T. Hara and G. Slade obtained using the lace expansion.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) CONACYT; NSERC
 
7. Date (YYYY-MM-DD) 2011-02-25
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1612
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1612
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 16
 
12. Language English=en
 
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