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2006 Convergence Results and Sharp Estimates for the Voter Model Interfaces
Samir Belhaouari, Thomas Mountford, Rongfeng Sun, Glauco Valle
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Electron. J. Probab. 11: 768-801 (2006). DOI: 10.1214/EJP.v11-349


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.


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Samir Belhaouari. Thomas Mountford. Rongfeng Sun. Glauco Valle. "Convergence Results and Sharp Estimates for the Voter Model Interfaces." Electron. J. Probab. 11 768 - 801, 2006.


Accepted: 29 August 2006; Published: 2006
First available in Project Euclid: 31 May 2016

zbMATH: 1113.60092
MathSciNet: MR2242663
Digital Object Identifier: 10.1214/EJP.v11-349

Primary: 60K35
Secondary: 60F17 , 82B24 , 82B41

Keywords: Brownian web , Coalescing random walks , invariance principle , voter model interface


Vol.11 • 2006
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