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FIELD
Mathematics
DATE
Dec 15 (Thu), 2022
TIME
10:00 ~ 11:00
PLACE
ONLINE
SPEAKER
Alberts, Thomas
HOST
Lee, Jaehun
INSTITUTE
University of Utah
TITLE
[GS_M_APP] 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.
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