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Probability and Computational Finance Seminar
Wei-Kuo Chen University of Chicago Title: On some Gaussian inequalities arising from the study of the Sherrington-Kirkpatrick mean-field spin glass. Abstract: This talk will be concentrated on some Gaussian inequalities arising naturally from the study of the Sherrington-Kirkpatrick model. We will first discuss the strict convexity of the Parisi functional and show that in the simplest case it gives a reverse form of the Prekopa-Leindler inequality. Next, we will present simple algebraic criteria that yield sharp Holder types of inequalities for the product of functions of Gaussian random vectors with arbitrary covariance structure. As an application, we will explain how our results unify several well-known inequalities in functional geometry, such as, the Brascamp-Lieb inequality, the sharp Young inequality, etc. Based on joint works with A. Auffinger, N. Dafnis, and G. Paouris. Date: Friday, December 5, 2014 Time: 4:30 pm Location: Wean Hall 8220 |