Probabilistic Operator Algebra Seminar: Freeness and asymptotic freeness in the context of tensors

Seminar | February 11 | 2-4 p.m. | 736 Evans Hall

 Benoit Collins, Kyoto University

 Department of Mathematics

It is known that the property of being free (or asymptotically free) for Haar unitaries remains to some extent, when the unitaries are tensored with other unitaries. In the recent years, we investigated the question of, to which extent this property holds. For example, does it hold when tensored by non-unitary operators ? When does asymptotic freeness hold strongly (in norm) ? In traffics ? etc. We have complete answers to some questions, and partial answers to others. I will review what is known at this point. This talk is based on various papers in collaboration with people including Charles Bordenave (CNRS), Camille Male (CNRS), and Pierre Ives Gaudreau Lamarre (Princeton).