S. Belhaouari, T. Mountford and G. Valle

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 $\alpha < 2$.

2000 Mathematics Subject Classification: 60G60 (primary), 60G17, 60G15 (secondary).

E-mail:
thomas.mountford@epfl.ch