2017/02/14 by Ilya Soloveychik, Xiang Yu, Soloveychik, Ilya +3 · 1 citation
Mathematics · Biochemistry, Genetics and Molecular Biology · Engineering · #Random Matrices and Applications #Fractal and DNA sequence analysis #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1702.04086
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=2m-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.