Spectral pseudorandomness and the road to improved clique number bounds for Paley graphs
D Kunisky - arXiv preprint arXiv:2303.16475, 2023 - arxiv.org
We study subgraphs of Paley graphs of prime order $ p $ induced on the sets of vertices
extending a given independent set of size $ a $ to a larger independent set. Using a …
extending a given independent set of size $ a $ to a larger independent set. Using a …
Kesten–McKay law for random subensembles of Paley equiangular tight frames
We apply the method of moments to prove a recent conjecture of Haikin, Zamir and Gavish
concerning the distribution of the singular values of random subensembles of Paley …
concerning the distribution of the singular values of random subensembles of Paley …
Symmetric pseudo-random matrices
I Soloveychik, Y Xiang, V Tarokh - IEEE Transactions on …, 2018 - ieeexplore.ieee.org
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 …
on the similarity of their spectra to Wigner's semicircular law. Using binary m-sequences …
Random matrices from linear codes and Wigner's semicircle law
CH Chan, E Kung, M Xiong - IEEE Transactions on Information …, 2019 - ieeexplore.ieee.org
In this paper, we consider a new normalization of matrices obtained by choosing distinct
codewords at random from linear codes over finite fields and find that under some natural …
codewords at random from linear codes over finite fields and find that under some natural …
Asymptotically Pseudo-Independent Matrices
I Soloveychik, V Tarokh - arXiv preprint arXiv:1809.00408, 2018 - arxiv.org
We show that the family of pseudo-random matrices recently discovered by Soloveychik,
Xiang, and Tarokh in their workSymmetric Pseudo-Random Matrices' exhibits asymptotic …
Xiang, and Tarokh in their workSymmetric Pseudo-Random Matrices' exhibits asymptotic …
Explicit symmetric pseudo-random matrices
I Soloveychik, Y Xiang, V Tarokh - 2017 IEEE Information …, 2017 - ieeexplore.ieee.org
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 …
on the similarity of their spectra to Wigner's semicircular law. Using binary m-sequences …
On the spectral norms of pseudo-wigner and related matrices
I Soloveychik, V Tarokh - 2017 55th Annual Allerton …, 2017 - ieeexplore.ieee.org
We investigate the spectral norms of symmetric N× N matrices from two pseudo-random
ensembles. The first is the pseudo-Wigner ensemble introduced in “Pseudo-Wigner …
ensembles. The first is the pseudo-Wigner ensemble introduced in “Pseudo-Wigner …
Spectral distribution of random matrices from mutually unbiased bases
CH Chan, M Xiong - arXiv preprint arXiv:1912.10031, 2019 - arxiv.org
We consider the random matrix obtained by picking vectors randomly from a large collection
of mutually unbiased bases of $\mathbb {C}^ n $, and prove that the spectral distribution …
of mutually unbiased bases of $\mathbb {C}^ n $, and prove that the spectral distribution …
Pseudo-wigner matrices from dual BCH codes
I Soloveychik, Y Xiang, V Tarokh - 2017 IEEE International …, 2017 - ieeexplore.ieee.org
We consider the problem of generating symmetric pseudo-random sign (±1) matrices based
on the similarity of their spectra to Wigner's semicircular law. We introduce r-independent …
on the similarity of their spectra to Wigner's semicircular law. We introduce r-independent …