arXiv 1702.040862017-02math.PR

Symmetric Pseudo-Random Matrices

Ilya Soloveychik, Yu Xiang, Vahid Tarokh

备注：: arXiv admin note: text overlap with arXiv:1701.05544

英文摘要：

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.

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