We introduce a new class of spatial-temporal point processes based on Voronoi
tessellations. At each step of such a process, a point is chosen at random according
to a distribution determined by the associated Voronoi cells. The point is then
removed, and a new random point is added to the configuration. The dynamics are simple
and intuitive and could be applied to modelling natural phenomena. We prove ergodicity
of these processes under wide conditions.
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