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Counting points in Determinantal and Permanental processes IIMathematical Physics & Probability
|Speaker: ||Manjunath Krishnapur, UC Berkeley, Dept of Statistics|
|Location: ||693 Kerr|
|Start time: ||Tue, Apr 19 2005, 3:10PM|
This is a continuation of the
Ben Hough's talk from April 12.
Determinantal or fermionic processes occur in Physics and in
Combinatorics. In recent work with Hough, Peres and Virag we realized
that the counting measure of a determinantal process has a strikingly
simple property. In this talk we introduce a criterion under which the
joint distribution of counts in several regions can be described
probabilistically, and apply this to certain processes in two dimensions
to obtain joint distributions of the absolute values of the points of the
process. In particular this applies to a family of invariant determinantal
processes in the sphere, in the plane and in the hyperbolic plane.