Convergence results and sharp estimates for the voter model interfaces

brahim belhaouari, samir and Thomas Mountford, TM and G. Valle, GV (2010) Convergence results and sharp estimates for the voter model interfaces. [Citation Index Journal]

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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 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 th moment is necessary for this convergence for all gamm 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

Item Type:Citation Index Journal
Impact Factor:33 .60
Subjects:Q Science > QA Mathematics > QA75 Electronic computers. Computer science
ID Code:2721
Deposited By: Dr Samir Brahim Belhaouari
Deposited On:21 Sep 2010 00:37
Last Modified:19 Jan 2017 08:25

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