Physique mathématique, Probabilités
Approximate Ground States of Hypercube Spin Glasses are Near Corners
Comptes Rendus. Mathématique, Tome 359 (2021) no. 9, pp. 1097-1105.

We show that with probability exponentially close to $1$, all near-maximizers of any mean-field mixed $p$-spin glass Hamiltonian on the hypercube ${\left[-1,1\right]}^{N}$ are near a corner. This confirms a recent conjecture of Gamarnik and Jagannath. The proof is elementary and extends to arbitrary polytopes with ${e}^{o\left({N}^{2}\right)}$ faces.

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DOI : https://doi.org/10.5802/crmath.240
Mark Sellke 1

1. Stanford University, Department of Mathematics, USA.
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Mark Sellke. Approximate Ground States of Hypercube Spin Glasses are Near Corners. Comptes Rendus. Mathématique, Tome 359 (2021) no. 9, pp. 1097-1105. doi : 10.5802/crmath.240. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.240/

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