Tracy-Widom law for the extreme eigenvalues of large signal-plus-noise matrices
Date: Thursday, 5 August 2021
Time: 11 am - 12 noon
Speaker: Zhixiang Zhang (Nanyang Technological University)
Abstract:
We study the asymptotic distribution for extreme eigenvalues of large signal-plus-noise type of matrices. Assume that the data matrix is S=R+X where the signal matrix R is allowed to be full rank and the noise matrix X contains i.i.d. standardized entries. Under some regularity conditions of the signal matrix R that assure the square root behavior of spectral density near the edge, we prove that the extreme eigenvalues of signal-plus-noise matrices have Tracy-Widom distribution under a tail condition of entries of X. Moreover, the tail condition is proved to be necessary and sufficient to assure the Tracy-Widom laws. Applications of our results on signal detection and data privacy will be discussed.
Zoom Link: Please contact Yanrong Yang (yanrong.yang@anu.edu.au) to obtain the zoom link for this seminar.