On the operator norm of tensors matrices involving Haar unitaries

Mathphys Analysis Seminar

I will introduce the problem of studying the operator norm of random matrices built from polynomial operations involving multiple iid Haar unitary random matrices or random permutation matrices. I will explain its relevance in free probability and other areas, known results, known limitations in the context of random tensors, and recent results in the case of tensors. Time allowing, I will describe the techniques involved (operator-valued non-backtracking theory). This is in part joint work with Charles Bordenave, and in particular, based on the recent preprint arXiv/2304.05714