On the Gaussian surface area of spectrahedra

2021/12/02 by Srinivasan Arunachalam, Oded Regev, Arunachalam, Srinivasan +3
Mathematics · #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.2112.01463

8 pages. v2: minor changes to improve presentation

openalex publication_date 2021/12/02 · arxiv created 2022/02/02 · arxiv updated 2022/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for sufficiently large n≥ 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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