Math @ Duke
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Publications [#336638] of Vahid Tarokh
Papers Published
- Soloveychik, I; Xiang, Y; Tarokh, V, Pseudo-Wigner Matrices,
Ieee Transactions on Information Theory, vol. 64 no. 4
(April, 2018),
pp. 3170-3178, Institute of Electrical and Electronics Engineers (IEEE) [doi]
(last updated on 2023/06/01)
Abstract: 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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