3:00 p.m., Friday (February 27th)

Math Annex 1100

Yuval Peres
University of California, Berkeley and Microsoft Research

Point processes, the stable marriage algorithm, and Gaussian power series

We consider invariant point processes, i.e., random collections of points with distribution invariant under isometries: the simplest example is the Poisson point process. Given a point process M in the plane, the Voronoi tesselation assigns a polygon (of different area) to each point of M. The geometry of "fair" allocations is much richer: There is a unique "fair" allocation that is "stable" in the sense of the Gale-Shapley stable marriage problem. Zeros of power series with Gaussian coefficients are a different source of point processes, where the isometry invariance is connected to classical complex analysis. In the case of independent coefficients with equal variance, the zeros form a determinantal process in the hyperbolic plane, with conformally invariant dynamics. Surprisingly, in this case the number of zeros in a disk has a coin-tossing interpretation. (Talk based on joint works with C. Hoffman, A. Holroyd and B. Virag).

Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).

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