Dr. Shannon Starr


McGill University


Thursday, February 19, 2004 - 11:00am


MSTB 254

Recently Michael Aizenman, Bob Sims and I formulated a
generalized variational principle (GVP) for the SK model and its
relatives. Our result is based on the recent developments of F. Guerra and
F. Toninelli, but is equally well motivated by the physicists' approach as
in the book by Parisi, Mezard and Virasoro. In this talk, I will give an
introduction to the SK model, describe the Parisi ansatz, and show how an
elementary, but little-known, fact about Gaussian processes implies the
GVP almost trivially. I will end with a brief description of some special
Poisson-Kingman distributions, called Poisson-Dirichlet processes,
$\textrm{PD}(\alpha,0)$ for $0