Sums of GUE Matrices and Concentration of Hives from Correlation Decay of Eigengaps

Explore a 48-minute lecture on the concentration of augmented hives associated with sums of random Hermitian matrices. Delve into the asymptotic analysis of random hives, focusing on eigenvalues drawn from the GUE ensemble. Examine key ingredients such as Speyer's representation of augmented hives, Klartag's results on the KLS conjecture, covariance bounds of eigenvalue gaps, and the application of determinantal processes to analyze the GUE minor process. Gain insights from this joint work presented by Hariharan Narayanan at IPAM's Integrability and Algebraic Combinatorics Workshop, covering advanced topics in mathematical physics and probability theory.