Tightness for the interfaces of one-dimensional voter models

S. Belhaouari; T. Mountford; G. Valle

doi:10.1112/plms/pdl016

Tightness for the interfaces of one-dimensional voter models

S. Belhaouari^*, T. Mountford, G. Valle

^*Corresponding author for this work

Swiss Federal Institute of Technology Lausanne

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

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 a for some α < 2.

Original language	English
Pages (from-to)	421-442
Number of pages	22
Journal	Proceedings of the London Mathematical Society
Volume	94
Issue number	2
DOIs	https://doi.org/10.1112/plms/pdl016
Publication status	Published - Mar 2007
Externally published	Yes

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author = "S. Belhaouari and T. Mountford and G. Valle",

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AB - 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 a for some α < 2.

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Tightness for the interfaces of one-dimensional voter models

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