Wednesday, May 4, 2022 - 09:00 in ZOOM - Video Conference
Phase transition of eigenvector for spiked random matrices
A talk in the Seminar Zufallsmatrizen series by
Zhigang Bao from Hong Kong University of Science and Technology
| Abstract: |
In this talk, we will first review some recent results on
the eigenvectors of random matrices under fixed-rank deformation, and
then we will focus on the limit distribution of the leading eigenvectors
of the Gaussian Unitary Ensemble (GUE) with fixed-rank (aka spiked)
external source, in the critical regime of the Baik-Ben Arous-Peche
(BBP) phase transition. The distribution is given in terms of a
determinantal point process with extended Airy kernel. Our result can be
regarded as an eigenvector counterpart of the BBP eigenvalue phase
transition. The derivation of the distribution makes use of the recently
rediscovered eigenvector-eigenvalue identity, together with the
determinantal point process representation of the GUE minor process with
external source. This is a joint work with Dong Wang (UCAS).
Please contact Anas Rahman (anas.rahman@live.com.au) for details regarding access.
Within the CRC this talk is associated to the project(s): C6 |
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