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Tightness for the interfaces of one-dimensional voter models. (English) Zbl 1112.60074
Summary: We show that for the voter model on $\{0,1\}^{\Bbb Z}$ 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 zeros and ones exists if $p(\cdot)$ has finite second moment but does not if $p(\cdot)$ fails to have finite moment of order $\alpha$ for some $\alpha<2$.

60K35Interacting random processes; statistical mechanics type models; percolation theory
60F17Functional limit theorems; invariance principles
82B41Random walks, random surfaces, lattice animals, etc. (statistical mechanics)
82B24Interface problems; diffusion-limited aggregation (equilibrium statistical mechanics)
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