Open Access
2008 Tightness of voter model interfaces
Anja Sturm, Jan Swart
Author Affiliations +
Electron. Commun. Probab. 13: 165-174 (2008). DOI: 10.1214/ECP.v13-1360


Consider a long-range, one-dimensional voter model started with all zeroes on the negative integers and all ones on the positive integers. If the process obtained by identifying states that are translations of each other is positively recurrent, then it is said that the voter model exhibits interface tightness. In 1995, Cox and Durrett proved that one-dimensional voter models exhibit interface tightness if their infection rates have a finite third moment. Recently, Belhaouari, Mountford, and Valle have improved this by showing that a finite second moment suffices. The present paper gives a new short proof of this fact. We also prove interface tightness for a long range swapping voter model, which has a mixture of long range voter model and exclusion process dynamics.


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Anja Sturm. Jan Swart. "Tightness of voter model interfaces." Electron. Commun. Probab. 13 165 - 174, 2008.


Accepted: 8 April 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1187.82088
MathSciNet: MR2399278
Digital Object Identifier: 10.1214/ECP.v13-1360

Primary: 82C22
Secondary: 60K35 , 82C24 , 82C41

Keywords: Exclusion process , interface tightness , Long range voter model , swapping voter model

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