| Título: | Convergence of Lattice Trees to Super-Brownian Motion above the Critical Dimension |
| Autores: | Holmes, Mark P.; U. Auckland |
| Fecha: | 2008-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Lattice trees; super-Brownian motion; lace expansion. 82B41; 60F05; 60G57; 60K35. |
| Descripción: | 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. |
| Idioma: | No aplica |
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