From the JUE to the Hermitian Jacobi process: finite and infinite sizes
A talk in the Seminar Zufallsmatrizen series by
Tarek Hamdi
| Abstract: | The Jacobi Unitary Ensemble (JUE) is a unitarily-invariant matrix model which
admits various relevant applications. One way to describe its joint law is by
taking the radial part of the compression by two orthogonal projections of a
Haar-distributed unitary matrix. This realization has proved useful in
understanding the JUE in statistical applications. To extend these results to the
dynamical setting, the hermitian Jacobi process was introduced by replacing the
Haar unitary matrix with a unitary Brownian motion. Despite the explicit
knowledge of joint law of its eigenvalues, determining its large-size limit (in the
sense of *-distribution) is notoriously difficult compared to the JUE ensemble.
In this talk, we will explore the spectral dynamics of the hermitian Jacobi process
in both finite and infinite dimensional settings. We will discuss different
approaches for computing its moments and determining the spectral
distribution of its large-size limit. Additionally, we will investigate dynamical
analogues for some results of the JUE and their applications to quantum
information theory. Please contact Lucas Hackl (Lucas.Hackl@unimelb.edu.au) for details regarding access Within the CRC this talk is associated to the project(s): C6 |