On the Gaussian surface area of spectrahedra

Abstract

We show that for sufficiently large $n\ge 1$ 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 $\Theta (n^{1/8})$ with high probability.

8 pages. v2: minor changes to improve presentation