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arXiv · 2310.14582

Free probability of type B prime

Katsunori Fujie·Takahiro Hasebe
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Abstract

Free probability of type B was invented by Biane--Goodman--Nica, and then it was generalized by Belinschi--Shlyakhtenko and F\'evrier--Nica to infinitesimal free probability. The latter found its applications to eigenvalues of perturbed random matrices in the work of Shlyakhtenko and C\'ebron--Dahlqvist--Gabriel. This paper offers a new framework, called ``free probability of type B${}^\prime$'', 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.

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Katsunori Fujie, Takahiro Hasebe. 2023-10-23. Free probability of type B prime. https://arxiv.org/abs/2310.14582

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