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Tightness of voter model interfaces

Authors
  • Sturm, Anja
  • Swart, Jan M.
Type
Preprint
Publication Date
Jul 11, 2007
Submission Date
Jun 29, 2007
Identifiers
arXiv ID: 0706.4405
Source
arXiv
License
Unknown
External links

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.

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