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Tightness for the interfaces of one‐dimensional voter models

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.