Approximate Ground States of Hypercube Spin Glasses are Near Corners [article]

Mark Sellke
2020 arXiv   pre-print
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