In this talk (which is joint work with Pei-Lun Tseng (NYU Abu Dhabi)) I will show that free independence can be adapted to give spectral results on finite rank perturbations of unitarily invariant matrix ensembles.

The main concepts are that of an infinitesimal operator (the finite rank perturbation) and infinitesimal independence (a non-commutative analogue of conditional independence). I will apply this to the commutator and anticommutator of independent operators.

Bio: James Mingo works on free probability and random matrix theory; you can see more about the subject from his book 'Free Probability and Random Matrices' volume 35 in the Fields Institute Monograph Series.