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 | PostScript
Copyright for articles published in this journal is retained by the authors, with first publication rights granted to the journal. By virtue of their appearance in this open access journal, articles are free to use, with proper attribution, in educational and other non-commercial settings.
The authors of papers published in EJP/ECP retain the copyright. We ask for the permission to use the material in any form. We also require that the initial publication in EJP or ECP is acknowledged in any future publication of the same article.
Before a paper is published in the Electronic Journal of Probability or Electronic Communications in Probability we must receive a hard-copy of the copyright form. Please mail it to
Philippe Carmona
Laboratoire Jean Leray UMR 6629
Universite de Nantes,
2, Rue de la Houssinière BP 92208
F-44322 Nantes Cédex 03
France
You can also send it by FAX: (33|0) 2 51 12 59 12 to the attention of Philippe Carmona.
The preferred way is to send a scanned (jpeg or pdf) copy of the signed copyright form to the managing editor Philippe Carmona at ejpecpme@math.univ-nantes.fr.
If a paper has several authors, the corresponding author signs the copyright form
on behalf of all the authors.