On the Gaussian surface area of spectrahedra

preprint2022arXivOpen access

We show that for sufficiently large $n\geq 1$ and $d=C n^{3/4}$ 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.

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On the Gaussian surface area of spectrahedra

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