Document Type
Lecture
Publication Date
3-26-2015
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 in progress with Raoul Normand and Balint Virag.
Relational Format
presentation
Recommended Citation
Alberts, Tom, "Random Geometry in the Spectral Measure of the Circular Beta Ensemble" (2015). Dynamical Systems Seminar. 15.
https://egrove.olemiss.edu/math_dynamical/15
