Wednesday, February 28, 2024 - 09:00 in ZOOM - Video Conference
Phase transition for the smallest eigenvalue of covariance matrices
A talk in the Seminar Zufallsmatrizen series by
Jaehun Lee from HKUST
| Abstract: |
Under the assumption of a finite fourth moment, the behavior of the
smallest eigenvalue in covariance matrices has been extensively
studied. In this talk, we explore the intriguing scenario where each
entry possesses an infinite fourth moment while still having a finite
second moment. We investigate the phase transition from Tracy-
Widom to Gaussian fluctuation for the smallest eigenvalue in this
context. Our proof strategy draws inspiration from the work of
Aggarwal, Lopatto, and Yau (2021), originally developed for the bulk
regime of the Lévy Wigner matrices. We extend and adapt their
approach to analyze the behavior of the smallest eigenvalue. Time-
permitting, we will also delve into a more heavy-tailed regime,
broadening the scope of our investigation. This is based on the joint
work with Zhigang Bao and Xiaocong Xu.
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 |
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