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Parisi's formula is a Hamilton-Jacobi equation in Wasserstein space

Probability 2019-07-03 v2 Disordered Systems and Neural Networks

Abstract

Parisi's formula is a self-contained description of the infinite-volume limit of the free energy of mean-field spin glass models. We show that this quantity can be recast as the solution of a Hamilton-Jacobi equation in the Wasserstein space of probability measures on the positive half-line.

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Cite

@article{arxiv.1906.08471,
  title  = {Parisi's formula is a Hamilton-Jacobi equation in Wasserstein space},
  author = {Jean-Christophe Mourrat},
  journal= {arXiv preprint arXiv:1906.08471},
  year   = {2019}
}

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19 pages