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Poissonian rain coloring and a selfsimilar process of coalescing planar partitionsSeminar: Probability Seminar  February 22  3:104 p.m.  1011 Evans Hall David Aldous, U. C. Berkeley Plant differently colored points in the plane; then let random points (``Poisson rain") fall, and give each new point the color of the nearest existing point. Previous investigation and simulations strongly suggest that the colored regions converge (in some sense) to a random partition of the plane. We prove a weak version of this, showing that normalized empirical measures converge to Lebesgue measures on a random partition into measurable sets. Topological properties remain an open problem. In the course of the proof, which heavily exploits timereversals, we encounter a novel selfsimilar process of coalescing planar partitions. In this process, sets A(z) in the partition are associated with Poisson random points z, and the dynamics are as follows. Points are deleted randomly at rate 1; when z is deleted, its set A(z) is adjoined to the set A(z') of the nearest other point z'. 5106422781 

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