##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability Seminar

## Tom Alberts

#### University of Utah

## Random Geometry in the Spectral Measure of the Circular Beta Ensemble

##### Abstract:

The Circular Beta Ensemble is a family of random unitary matrices whose eigenvalue distribution plays an important role in statistical physics. The spectral measure is a canonical way of describing the unitary matrix that takes into account the full operator, not just its eigenvalues. When the matrix is infinitely large (i.e. an operator on some infinite-dimensional Hilbert space) the spectral measure is supported on a fractal set and has a rough geometry on all scales. This talk will describe the analysis of these fractal properties. Joint work with Raoul Normand and Balint Virag.

Host: Todd Kemp

### April 14, 2016

### 10:00 AM

### AP&M 7321

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