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Mathematics Senior Thesis Defense by Stephen Willis '22
An Entropy Approach to the Investigation of the Distribution of the Eigenvalues for Random Unitary Matrices by Stephen Willis ’22, Mathematics Senior Thesis Defense, Tuesday, May 17, 1:40 – 2:15 pm, North Science Building 113, Wachenheim.
Abstract: The circular beta ensemble describes a family of random points which exhibit pairwise repulsion at a certain quantifiable rate. It is possible to construct families of random unitary matrices which have the circular beta ensemble as their eigenvalue point process. We calculate the entropy associated with this process and investigate the transition in the eigenvalue distribution (from small to large beta) from the perspective of the entropy.