Free probability of type B prime
arXiv:2310.14582
Abstract
Free probability of type B was invented by Biane--Goodman--Nica, and then it was generalized by Belinschi--Shlyakhtenko and Février--Nica to infinitesimal free probability. The latter found its applications to eigenvalues of perturbed random matrices in the work of Shlyakhtenko and Cébron--Dahlqvist--Gabriel. This paper offers a new framework, called ``free probability of type B'', which appears in the large size limit of independent unitarily invariant random matrices with perturbations. Our framework is related to boolean, free, (anti)monotone, cyclic-(anti)monotone and conditionally free independences. We then apply the new framework to the principal minor of unitarily invariant random matrices, which leads to the definition of a multivariate inverse Markov--Krein transform.
24 pages; Revision from reviewer comments