Colloquium
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 GaleShapley 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 cointossing 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).
