Limiting Empirical Singular Value Distribution of Restrictions of Unitary Matrices
Brendan Farrell
TL;DR
This paper analyzes the asymptotic behavior of singular values for submatrices of random unitary matrices, including Haar and DFT matrices, after random row and column removal.
Contribution
It provides the first characterization of the limiting empirical singular value distribution for these restricted matrices.
Findings
Derived the limiting distribution for Haar-distributed unitary matrices.
Extended results to discrete Fourier transform matrices.
Offers insights into the spectral properties of submatrices after random restrictions.
Abstract
We determine the limiting empirical singular value distribution for random unitary matrices with Haar distribution and discrete Fourier transform (DFT) matrices when a random set of columns and rows is removed.
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Taxonomy
TopicsRandom Matrices and Applications · Advanced Algebra and Geometry · Graph theory and applications