Around the Joint Behavior of Independent Random Tensor Matrices - Lecture 3

Explore the third lecture in a series on the joint behavior of independent random tensor matrices, delivered by Benoit Collins at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into advanced topics in free probability theory and its extensions to tensor structures with smaller symmetry groups. Examine the case where invariants are tensors of local unitaries, including generalizations of unitary Weingarten calculus and HCIZ integrals. Investigate scenarios where symmetries are represented by irreducible representations of the unitary group. Gain insights into new techniques for studying analytic properties of matrices, such as typical operator norms. Engage with open questions and cutting-edge research in this hour-long exploration of random matrix theory and non-commutative geometry.