| Título: | Convergence Results and Sharp Estimates for the Voter Model Interfaces |
| Autores: |
Belhaouari, Samir; EPFL Mountford, Thomas; EPFL Sun, Rongfeng; EURANDOM Valle, Glauco; EPFL / DME-IM-UFRJ |
| Fecha: | 2006-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
voter model interface, coalescing random walks, Brownian web, invariance principle 60K35, 82B24, 82B41, 60F17 |
| Descripción: | We study the evolution of the interface for the one-dimensional voter model. We show that if the random walk kernel associated with the voter model has finite $\gamma$-th moment for some $\gamma > 3$, then the evolution of the interface boundaries converge weakly to a Brownian motion under diffusive scaling. This extends recent work of Newman, Ravishankar and Sun. Our result is optimal in the sense that finite $\gamma$-th moment is necessary for this convergence for all $\gamma \in (0,3)$. We also obtain relatively sharp estimates for the tail distribution of the size of the equilibrium interface, extending earlier results of Cox and Durrett, and Belhaouari, Mountford and Valle. |
| Idioma: | No aplica |
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