Groups and Operator Algebras Seminar
Speaker: Nicolas Gilliers (Université Paris-Cité)
Title: Asymptotic cyclic conditional freeness of random matrices
Abstract: Voiculescu's freeness emerges when computing the asymptotic spectra of polynomials on random matrices with eigenspaces in generic positions, where they are randomly rotated using a uniform unitary random matrix.
We elaborate on this fundamental result by proposing a random matrix model, which we name the Vortex model, where U_N has the law of a uniform unitary random matrix but is conditioned to leave invariant a deterministic vector. In the high-dimensional regime, this model exhibits asymptotic conditional freeness.
If time permits, we will introduce cyclic-conditional freeness, which unifies three independences: infinitesimal freeness, cyclic monotone independence, and cyclic Boolean independence. Infinitesimal distributions in the Vortex model can be computed thanks to this new independence.