Tightness of voter model interfaces

Details Tightness of voter model interfaces Tightness of voter model interfaces

2007-06-29

arxiv.org/abs/0706.4405v2

Mathematics

Probability

Corrected a serious error in Lemma 3. Some additional insignificant corrections. 9 pages

Scientific paper

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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