Random subsets of structured deterministic frames have MANOVA spectra.

ABSTRACT: We draw a random subset of [Formula: see text] rows from a frame with [Formula: see text] rows (vectors) and [Formula: see text] columns (dimensions), where [Formula: see text] and [Formula: see text] are proportional to [Formula: see text] For a variety of important deterministic equiangular tight frames (ETFs) and tight non-ETFs, we consider the distribution of singular values of the [Formula: see text]-subset matrix. We observe that, for large [Formula: see text], they can be precisely described by a known probability distribution-Wachter's MANOVA (multivariate ANOVA) spectral distribution, a phenomenon that was previously known only for two types of random frames. In terms of convergence to this limit, the [Formula: see text]-subset matrix from all of these frames is shown to be empiri

SUBMITTER: Haikin M 

PROVIDER: S-EPMC5495238 | biostudies-literature | 2017 Jun

REPOSITORIES: biostudies-literature