Tightness for the interfaces of one-dimensional voter models

Details Tightness for the interfaces of one-dimensional voter models Tightness for the interfaces of one-dimensional voter models

2006-08-28

arxiv.org/abs/math/0608690v1

Mathematics

Probability

20 pages

Scientific paper

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 $\alpha$ for some $\alpha <2$.

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