Boris Khoruzhenko

Eigenvalues of truncated unitary symplectic matrices

Draw a matrix at random from one of the classical compact groups of large dimension and remove an equal number of rows and columns from it. What can be said about the distribution of eigenvalues of the truncated matrix? This question for the complex unitary group was addressed by Sommers and Zyczkowski in their pioneering paper in 2000. The real orthogonal case was addressed by a number of research groups and is, nowadays, well understood too. Surprisingly, little was known about the remaining case of the unitary symplectic matrices. In the first part of this talk I will explain why truncations of unitary symplectic matrices are interesting too, and in the second part I will describe the distribution of their complex eigenvalues in the regimes of weak and strong non-unitarity and explain some analytic challenges of getting asymptotics of the eigenvalue correlation functions in planar symplectic ensembles.

Talk recording: https://mediasite.bris.ac.uk/Mediasite/Play/9486d1aac46e4242b538d12f74d462a51d