A dynamic programming approach to the Parisi functional

@article{Jagannath2015ADP,
  title={A dynamic programming approach to the Parisi functional},
  author={Aukosh Jagannath and Ian Tobasco},
  journal={arXiv: Probability},
  year={2015},
  volume={144},
  pages={3135-3150}
}
  • Aukosh Jagannath, Ian Tobasco
  • Published 2015
  • Mathematics, Physics
  • arXiv: Probability
  • G.Parisi predicted an important variational formula for the thermodynamic limit of the intensive free energy for a class of mean field spin glasses. In this paper, we present an elementary approach to the study of the Parisi functional using stochastic dynamic programing and semi-linear PDE. We give a derivation of important properties of the Parisi PDE avoiding the use of Ruelle Probability Cascades and Cole-Hopf transformations. As an application, we give a simple proof of the strict… CONTINUE READING
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