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Approximate Ground States of Hypercube Spin Glasses are Near Corners
[article]
2020
arXiv
pre-print
Preserved Fulltext
We show that with probability exponentially close to 1, all near-maximizers of any mean-field mixed p-spin glass Hamiltonian on the hypercube [-1,1]^N are near a corner. This confirms a recent conjecture of Gamarnik and Jagannath. The proof is elementary and generalizes to arbitrary polytopes with e^o(N^2) faces.
arXiv:2009.09316v1
fatcat:33xy5zaefba5jp6nd5bqzeka6q