Title: Grothendieck L_p problem for Gaussian matrices
Speaker: Arnab Sen
Speaker Info: University of Minnesota
Consider the optimization problem where we maximize the quadratic form of a large Gaussian matrix over the unit L_p ball. The case p = 2 corresponds to the top eigenvalue of the Gaussian Orthogonal Ensemble. On the other hand, when p = ∞, the maximum value is the ground state energy of the mean-field Ising spin glass model and its limit can be expressed by the Parisi formula. In the talk, I will describe the limit of this optimization problem for general p and discuss some results on the behavior of optimizers along with some open problems.Date: Wednesday, January 20, 2021
This is joint work with Wei-Kuo Chen.