##### Department of Mathematics,

University of California San Diego

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### Math 243, Functional Analysis Seminar

## Jennifer Pi

#### University of California, Irvine

## Conditional Microstates and Non-Microstates Free Entropy: How are they related?

##### Abstract:

Voiculescu developed two main candidates for the analogs of entropy in free probability: the microstates and non-microstates free entropies. In 2003, Biane-Capitaine-Guionnet established a relationship between the two: the microstates free entropy is always bounded above by the non-microstates free entropy. In this talk, we discuss the conditional versions of these notions of free entropy. Then, by connecting each of the free entropies with the asymptotics of their classical counterparts, we provide an elementary proof of the result of Biane-Capitaine-Guionnet. This is joint work with David Jekel.

Host: David Jekel

### May 9, 2023

### 11:00 AM

APM 6402 and Zoom

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