On the Gaussian surface area of spectrahedra

Published 2 Dec 2021 in math.PR | (2112.01463v2)

Abstract: We show that for sufficiently large $n\geq 1$ and $d=C n<sup>{3/4}$ for some universal constant $C>0$, a random spectrahedron with matrices drawn from Gaussian orthogonal ensemble has Gaussian surface area $\Theta(n<sup>{1/8})$ with high probability.

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