Symmetric Pseudo-Random Matrices
Probability
2018-02-27 v8
Abstract
We consider the problem of generating symmetric pseudo-random sign (+/-1) matrices based on the similarity of their spectra to Wigner's semicircular law. Using binary m-sequences (Golomb sequences) of lengths n=2^m-1, we give a simple explicit construction of circulant n by n sign matrices and show that their spectra converge to the semicircular law when n grows. The Kolmogorov complexity of the proposed matrices equals to that of Golomb sequences and is at most 2log(n) bits.
Cite
@article{arxiv.1702.04086,
title = {Symmetric Pseudo-Random Matrices},
author = {Ilya Soloveychik and Yu Xiang and Vahid Tarokh},
journal= {arXiv preprint arXiv:1702.04086},
year = {2018}
}
Comments
arXiv admin note: text overlap with arXiv:1701.05544