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 Electronic Communications in Probability > Vol. 13 (2008) > Paper 16 open journal systems 


Tightness of voter model interfaces

Anja Sturm, University of Delaware
Jan M. Swart, 'UTIA


Abstract
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.


Full text: PDF

Pages: 165-174

Published on: April 8, 2008
Bibliography
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Electronic Communications in Probability. ISSN: 1083-589X