# On the Gaussian surface area of spectrahedra

@article{Arunachalam2021OnTG, title={On the Gaussian surface area of spectrahedra}, author={Srinivasan Arunachalam and Oded Regev and Penghui Yao}, journal={Electron. Colloquium Comput. Complex.}, year={2021}, volume={28}, pages={178} }

We show that for suﬃciently large n ≥ 1 and d = Cn 3 / 4 for some universal constant C > 0, a random spectrahedron with matrices drawn from Gaussian orthogonal ensemble has Gaussian surface area Θ( n 1 / 8 ) with high probability.

## One Citation

### Positive spectrahedra: invariance principles and pseudorandom generators

- MathematicsSTOC
- 2022

An invariance principle for positive spectrahedra is proved via the well-known Lindeberg method, an upper bound on noise sensitivity and a Littlewood-Offord theorem are proved and applications are given for constructing PRGs forpositive spectahedra, learning theory, discrepancy sets for positiveSpectrahedRA (over the Boolean cube) andPRGs for intersections of structured polynomial threshold functions.

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An invariance principle for positive spectrahedra is proved via the well-known Lindeberg method, an upper bound on noise sensitivity and a Littlewood-Offord theorem are proved and applications are given for constructing PRGs forpositive spectahedra, learning theory, discrepancy sets for positiveSpectrahedRA (over the Boolean cube) andPRGs for intersections of structured polynomial threshold functions.

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% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn%…

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