Strong convergence of tensor products of independent GUE matrices

Abstract: Given tuples of properly normalized independent NxN GUE matrices (X_1,…,X_r) and (Y_1,…,Y_s), we proved that the tuple (X_1⊗I,…,X_r⊗I,I⊗Y_1,…,I⊗Y_s) of matrices converges strongly as N tends to infinity. We will present the key steps and ideas of the proof. Note that it was shown by B. Hayes that this result implies that the Peterson-Thom conjecture is true. This is a joint work with Serban Belinschi.

mathematical physicscombinatoricsprobabilitystatistics theory

Audience: researchers in the topic

Abu Dhabi Stochastics Seminar