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Tightness for the interfaces of one‐dimensional voter models
Author(s) -
Belhaouari S.,
Mountford T.,
Valle G.
Publication year - 2007
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdl016
Subject(s) - unanimity , mathematics , moment (physics) , kernel (algebra) , random walk , order (exchange) , second moment of area , combinatorics , statistics , geometry , physics , classical mechanics , finance , political science , law , economics
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 α for some α < 2.
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