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Counting points in determinantal processes I
Probability| Speaker: | J. Ben Hough, UC Berkeley, Department of Mathematics |
| Location: | 693 Kerr |
| Start time: | Tue, Apr 12 2005, 3:10PM |
Description
Determinantal processes arise in physics (fermions, eigenvalues of random
matrices) and in combinatorics (nonintersecting paths, random spanning
trees). They have the striking property (Pauli's exclusion principle) that
the number of points in any subregion is a sum of independent Bernoulli
random variables. Moreover, any determinantal process can be represented as
a mixture of determinantal projection processes. We use these facts to
give simple probabilistic proofs of existence criteria for determinantal
processes and central limit theorems. Analogous results will be given for
permanental processes with geometric variables replacing the Bernoulli
variables. This is joint work with Manjunath Krishnapur, Yuval Peres and
Balint Virag.