English

Approximate Ground States of Hypercube Spin Glasses are Near Corners

Probability 2021-08-16 v2

Abstract

We show that with probability exponentially close to 11, all near-maximizers of any mean-field mixed pp-spin glass Hamiltonian on the hypercube [1,1]N[-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 eo(N2)e^{o(N^2)} faces.

Keywords

Cite

@article{arxiv.2009.09316,
  title  = {Approximate Ground States of Hypercube Spin Glasses are Near Corners},
  author = {Mark Sellke},
  journal= {arXiv preprint arXiv:2009.09316},
  year   = {2021}
}