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Explore the joint behavior of independent random tensor matrices in this advanced mathematics lecture. Delve into the extension of free probability theory to cases with smaller symmetry groups, focusing on matrices with tensor structure and symmetries given by tensors of chosen 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 an image of the unitary group under an irreducible representation. Discover new techniques for studying analytic properties of matrices, such as typical operator norms, within the realm of free probability theory. Gain insights into open questions and potential generalizations of free probability theory in this comprehensive exploration of random tensor matrices.
