Home | Contents | Submissions, editors, etc. | Login | Search | EJP
 Electronic Communications in Probability > Vol. 13 (2008) > Paper 16 open journal systems 

Tightness of voter model interfaces

Anja Sturm, University of Delaware
Jan M. Swart, 'UTIA

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

Pages: 165-174

Published on: April 8, 2008

  1. 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 1811747 Zbl 0978.60105
  2. 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 2242663 Zbl 1113.60092
  3. 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 2308233 Zbl 1112.60074
  4. J.T. Cox and R. Durrett. Hybrid zones and voter model interfaces. Bernoulli 1(4): 343--370, 1995. Math. Review 1369166 Zbl 0849.60088
  5. S.J. Handjani. The complete convergence theorem for coexistent threshold voter models. Ann. Probab. 27(1): 226--245, 1999. Math. Review 1681118 Zbl 0974.60093
  6. T.M. Liggett. Interacting Particle Systems. Springer, New York, 1985. Math. Review 0776231 Zbl 0559.60078
  7. A. Sturm and J.M. Swart. Voter models with heterozygosity selection. Ann. Appl. Probab 18(1): 59--99, 2008. Math. Review number not available.

Support Tool
Capture Cite
View Metadata
Printer Friendly
Author Address
Email Author
Email Others

Home | Contents | Submissions, editors, etc. | Login | Search | EJP

Electronic Communications in Probability. ISSN: 1083-589X