# Explicit near-fully X-Ramanujan graphs

@article{ODonnell2020ExplicitNX, title={Explicit near-fully X-Ramanujan graphs}, author={R. O'Donnell and Xinyu Wu}, journal={2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)}, year={2020}, pages={1045-1056} }

Let p(Y1, …, Yd, Z1, …, Ze) be a self-adjoint noncommutative polynomial, with coefficients from $\mathrm{C}^{\mathrm{r}\times \mathrm{r}}$, in the indeterminates Y1,…, Yd (considered to be self-adjoint), the indeterminates Z1, …, Ze, and their adjoints Z1*, …, Ze*. Suppose Y1, …, Yd are replaced by independent random n x n matching matrices, and Z1, …, Ze are replaced by independent random n x n permutation matrices. Assuming for simplicity that p's coefficients are 0–1 matrices, the result can… Expand

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