The Spectrum of an Hermitian Matrix With Dependent Entries Constructed from Random Independent Images
The Spectrum of an Hermitian Matrix With Dependent Entries Constructed from Random Independent Images

Amit Singer and Xiuyuan Cheng, Princeton University
Fine Hall 401
In this talk we will present a preliminary analysis and numerical results for the distribution of eigenvalues of a certain random N by N Hermitian matrix, whose construction is motivated by a problem in structural biology. The matrix is built from N images, where each image is an array of P pixels, and the pixels are i.i.d standard Gaussians. Numerical experiments suggest that the spectrum approaches Wigner's semicircle law for P>>N, but differs significantly from the semicircle for P