A ug 2 00 6 TIGHTNESS FOR THE INTERFACES OF ONE-DIMENSIONAL VOTER MODELS

Abstract

We show that for the voter model on {0, 1} 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 0’s and 1’s 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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