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 | |
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 | |
14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
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