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

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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 semi-circle law for P>>N, but differs significantly from the semi-circle for P