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Zbl 1112.60074
Belhaouari, S.; Mountford, T.; Valle, G.
Tightness for the interfaces of one-dimensional voter models. (English)
[J] Proc. Lond. Math. Soc. (3) 94, No. 2, 421-442 (2007). ISSN 0024-6115; ISSN 1460-244X/e

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 $\alpha<2$.

MSC 2000:: *60K35 Interacting random processes
60F17 Functional limit theorems
82B41 Random walks, etc. (statistical mechanics)
82B24 Interface problems (equilibrium)

Cited in: Zbl 1113.60092

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