The Parisi formula is a Hamilton-Jacobi equation in Wasserstein space

Jean Christophe Mourrat

Research output: Contribution to journalArticlepeer-review

Abstract

The Parisi formula is a self-contained description of the infinite-volume limit of the free energy of mean-field spin glass models. We showthat 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.

Original languageEnglish (US)
Pages (from-to)607-629
Number of pages23
JournalCanadian Journal of Mathematics
Volume74
Issue number3
DOIs
StatePublished - Jun 28 2022

Keywords

  • Hamilton Jacobi equation
  • Spin glass
  • Wasserstein space

ASJC Scopus subject areas

  • General Mathematics

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