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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.18620 |
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Table of Contents:
- We study the standard quadratic optimization problem over the simplex when the objective matrix is drawn from the Gaussian Orthogonal Ensemble (GOE). Let \(κ_n\) denote the support size of the almost surely unique global optimizer. We prove \[ \Prob(κ_n>1)\sim 2\sqrt{2π}\,\frac{\sqrt{\log n}}{n}. \] The proof combines an exact two-coordinate condition for edge improvement with a product formula obtained by conditioning on the diagonal order statistics. Boundary-layer estimates identify the leading contribution and show that supports of size at least three are negligible. Consequently, the minimum-diagonal vertex is globally optimal with probability tending to one, with an explicit first-order correction.