Applied Math And Analysis Seminar
Monday, September 5, 2016, 4:30pm, 119 Physics
Xiuyuan Cheng (Yale University)
Limiting Spectrum of Random Kernel Matrices

Abstract:

We consider n-by-n matrices whose (i, j)-th entry is f(X_i^T X_j), where X_1, ...,X_n are i.i.d. standard Gaussian random vectors in R^p, and f is a real-valued function. The eigenvalue distribution of these kernel random matrices is studied in the "large p, large n" regime. It is shown that with suitable normalization the spectral density converges weakly, and we identify the limit. Our analysis applies as long as the rescaled kernel function is generic, and particularly, this includes non-smooth functions, e.g. Heaviside step function. The limiting densities "interpolate" between the Marcenko-Pastur density and the semi-circle density. [video]

---

Generated at 3:07am Wednesday, April 24, 2024 by Mcal.   Top * Reload * Login