Wednesday, February 3, 2021 - 10:00 in ZOOM - Video Conference
Random states arising from the unitary Brownian motion and Jacobi polynomials in the simplex
A talk in the Seminar Zufallsmatrizen series by
Nizar Demni from Aix-Marseille University
| Abstract: |
I'll talk about a problem motivated by quantum information theory and raised by Nechita and Pellegrini. They asked to compute the joint distribution of a sub-vector of a random vector in the unit sphere sampled from the heat kernel.
For a single coordinate, the solution is expressed as a bilinear series of Jacobi polynomials and more generally, it involves the so-called Jacobi polynomials in the simplex introduced by Koorwinder. I'll exhibit the approach used by Nechita and Pellegrini based on pde's and the one I used to completely solve the problem and based on the decomposition of unitary spherical harmonics under the action of unitary subgroups.
Please contact Anas Rahman (anas.rahman@live.com.au) for details regarding access.
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