Pseudo-Wigner Matrices
We consider the problem of generating pseudo-random matrices based on the similarity of their spectra to Wigner's semicircular law. We introduce the notion of an r -independent pseudo-Wigner matrix ensemble and prove the closeness of the spectra of its matrices to the semicircular density in the Kolmogorov distance. We give an explicit construction of a family of N × N pseudo-Wigner ensembles using dual BCH codes and show that the Kolmogorov complexity of the obtained matrices is of the order of log(N) bits for a fixed designed Kolmogorov distance precision. We compare our construction with the quasi-random graphs introduced by Chung et al. and demonstrate that the pseudo-Wigner matrices pass stronger randomness tests than the adjacency matrices of these graphs (lifted by the mapping 0 → 1 and 1 → -1 ) do. Finally, we provide numerical simulations verifying our theoretical results.
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Related Subject Headings
- Networking & Telecommunications
- 4613 Theory of computation
- 4006 Communications engineering
- 1005 Communications Technologies
- 0906 Electrical and Electronic Engineering
- 0801 Artificial Intelligence and Image Processing
Citation
Published In
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Networking & Telecommunications
- 4613 Theory of computation
- 4006 Communications engineering
- 1005 Communications Technologies
- 0906 Electrical and Electronic Engineering
- 0801 Artificial Intelligence and Image Processing