On Gaussian inequalities for product of functions
Vortrag von Prof. Dr. Wei-Kuo Chen
Sprecher eingeladen von: Prof. Dr. Erwin Bolthausen
Datum: 23.10.13 Zeit: 17.15 - 18.15 Raum: ETH
Gaussian inequalities have played important roles in various scientific areas. In this talk, 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 yield several famous inequalities in functional geometry, such as, the Brascamp-Lieb inequality, the sharp Young inequality, etc. This part of the talk is based on the recent joint work with N. Dafnis and G. Parious. Along this direction, we will discuss a conjecture on the convexity of the Parisi functional arising from the study of the Sherrington-Kirkpatrick model in spin glass.