Optimization of the Sherrington-Kirkpatrick Hamiltonian

@article{Montanari2019OptimizationOT,
  title={Optimization of the Sherrington-Kirkpatrick Hamiltonian},
  author={Andrea Montanari},
  journal={2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)},
  year={2019},
  pages={1417-1433}
}
  • A. Montanari
  • Published 28 December 2018
  • Computer Science
  • 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)
Let A be a symmetric random matrix with independent and identically distributed Gaussian entries above the diagonal. We consider the problem of maximizing the quadratic form associated to A over binary vectors. In the language of statistical physics, this amounts to finding the ground state of the Sherrington-Kirkpatrick model of spin glasses. The asymptotic value of this optimization problem was characterized by Parisi via a celebrated variational principle, subsequently proved by Talagrand… 
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