##### Department of Mathematics,

University of California San Diego

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### Math 243 - Functional Analysis Seminar

## Ian Charlesworth

#### UCSD

## Bi-free probability and an approach to conjugate variables.

##### Abstract:

I will discuss some recent ongoing work with Paul Skoufranis to create a non-microstates bi-free entropy. I will propose a definition of bi-free conjugate variables and bi-free Fisher information, which admit desirable properties such as additivity in the presence of bi-free independence and versions of Cramer-Rao and Stam inequalities. I will also discuss the analogue of the free difference quotient, and some of the quirks present in the bi-free setting.

Host: Adrian Ioana

### November 30, 2017

### 1:00 PM

### AP&M 6218

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