Electronic Communications in Probability

Tightness of voter model interfaces

Anja Sturm and Jan Swart

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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.

Article information

Electron. Commun. Probab., Volume 13 (2008), paper no. 16, 165-174.

Accepted: 8 April 2008
First available in Project Euclid: 6 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 82C22: Interacting particle systems [See also 60K35]
Secondary: 82C24: Interface problems; diffusion-limited aggregation 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Long range voter model swapping voter model interface tightness exclusion process

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Sturm, Anja; Swart, Jan. Tightness of voter model interfaces. Electron. Commun. Probab. 13 (2008), paper no. 16, 165--174. doi:10.1214/ECP.v13-1360. https://projecteuclid.org/euclid.ecp/1465233443

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