##### Department of Mathematics,

University of California San Diego

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### Math 243 - Operator Algebras

## Ian Charlesworth

#### UCLA

## An alternating moment condition and liberation for bi-freeness

##### Abstract:

Bi-free probability is a generalization of free probability to study pairs of left and right faces in a non-commutative probability space. In this talk, I will demonstrate a characterization of bi-free independence inspired by the ``vanishing of alternating centred moments'' condition from free probability. I will also show how these ideas can be used to introduce a bi-free unitary Brownian motion and a liberation process which asymptotically creates bi-free independence.

Hosts: Adrian Ioana and Todd Kemp

### February 28, 2017

### 1:00 PM

### AP&M 5402

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