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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title = "Tightness for the interfaces of one-dimensional voter models",

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.",

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

year = "2007",

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AU - Belhaouari, S.

AU - Mountford, T.

AU - Valle, G.

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N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/42449135772

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DO - 10.1112/plms/pdl016

M3 - Article

AN - SCOPUS:42449135772

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EP - 442

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 2

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Tightness for the interfaces of one-dimensional voter models

Abstract

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