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.

V. Belitsky, P.A. Ferrari, M.V. Menshikov, and S.Y. Popov.
A mixture of the exclusion process and the voter model.
Bernoulli 7(1): 119--144, 2001.
Math. Review 1811747Zbl 0978.60105

S. Belhaouari, T. Mountford, R.Sun, and G. Valle.
Convergence results and sharp estimates for the voter model interfaces.
Electron. J. Probab. 11: Paper No. 30, 768--801, 2006.
Math. Review 2242663Zbl 1113.60092

S. Belhaouari, T. Mountford, and G. Valle.
Tightness for the interfaces of one-dimensional voter models.
Proc. Lond. Math. Soc. (3) 94(2): 421--442, 2007.
Math. Review 2308233Zbl 1112.60074