@article{EJP349,
author = {Samir Belhaouari and Thomas Mountford and Rongfeng Sun and Glauco Valle},
title = {Convergence Results and Sharp Estimates for the Voter Model Interfaces},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {11},
year = {2006},
keywords = {voter model interface, coalescing random walks, Brownian web, invariance principle},
abstract = {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.},
pages = {no. 30, 768-801},
issn = {1083-6489},
doi = {10.1214/EJP.v11-349},
url = {http://ejp.ejpecp.org/article/view/349}}