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Tightness for the interfaces of one-dimensional voter models

Samir Belhaouari·Thomas Mountford·Glauco Valle
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Abstract

We show that for the voter model on $\{0,1\}^{\mathbb{Z}}$ corresponding to a random walk with kernel $p(\cdot)$ and starting from unanimity to the right and opposing unanimity to the left, a tight interface between 0's and 1's exists if $p(\cdot)$ has finite second moment but does not if $p(\cdot)$ fails to have finite moment of order $α$ for some $α<2$.

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Samir Belhaouari, Thomas Mountford, Glauco Valle. 2006-08-28. Tightness for the interfaces of one-dimensional voter models. https://arxiv.org/abs/math/0608690

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