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Proceedings of the London Mathematical Society Advance Access published online on December 5, 2006
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdl016
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© 2006 London Mathematical Society

Tightness for the interfaces of one-dimensional voter models

S. Belhaouari, T. Mountford and G. Valle

Département de Mathématiques, École Polytechnique Fédérale, 1015 Lausanne, Switzerland, thomas.mountford{at}epfl.ch, samir.brahim{at}epfl.ch, glauco.valle{at}epfl.ch

Received 3 March 2005. Revision received 10 May 2006.

We show that for the voter model on {0, 1}Z corresponding to a random walk with kernel p(·) and starting from unanimity to the right and opposing unanimity to the left, a tight interface between zeros and ones exists if p(·) has finite second moment but does not if p(·) fails to have finite moment of order {alpha} for some {alpha}<2.


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