Consider a one-dimensional long-range voter model started with all
zeroes on the negative integers and all ones on the positive
integers. Such a process models the interface between two infinite,
genetically different populations, in the absence of selection. We may
ask whether the area where the two types mix grows in time, or stays
stochastically bounded. In the latter case one says that interface
tightness holds. In this talk, I will discuss sufficient conditions
for interface tightness derived by Cox and Durrett, by Belhaouari,
Mountford and Valle, and most recently by Anja Sturm and myself. It
will turn out that a finite second moment of the infection rates
suffices.
