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Tightness of voter model interfaces
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SYSNO ASEP 0309104 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Tightness of voter model interfaces Title Tuhost rozhranní modelů voličů Author(s) Sturm, A. (US)
Swart, Jan M. (UTIA-B) RID, ORCIDSource Title Electronic Communications in Probability - ISSN 1083-589X
Roč. 13, - (2008), s. 165-174Number of pages 10 s. Language eng - English Country US - United States Keywords long range voter model ; swapping voter model ; interface tightness ; exclusion process Subject RIV BD - Theory of Information R&D Projects GA201/06/1323 GA ČR - Czech Science Foundation (CSF) GA201/07/0237 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10750506 - UTIA-B (2005-2011) UT WOS 000254747900001 Annotation Consider a long-range, one-dimensional voter model started with all zeros 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. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2009
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