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

Jean Christophe Mourrat

doi:10.4153/S0008414X21000031

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

Jean Christophe Mourrat

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	607-629
Number of pages	23
Journal	Canadian Journal of Mathematics
Volume	74
Issue number	3
DOIs	https://doi.org/10.4153/S0008414X21000031
State	Published - Jun 28 2022

Keywords

Hamilton Jacobi equation
Spin glass
Wasserstein space

ASJC Scopus subject areas

Mathematics(all)

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10.4153/S0008414X21000031

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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.",

keywords = "Hamilton Jacobi equation, Spin glass, Wasserstein space",

author = "Mourrat, {Jean Christophe}",

note = "Funding Information: This work was partially supported by the ANR grants LSD (ANR-15-CE40-0020-03) and Malin (ANR-16-CE93-0003). Publisher Copyright: {\textcopyright} Canadian Mathematical Society 2021.",

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Y1 - 2022/6/28

N2 - 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.

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KW - Spin glass

KW - Wasserstein space

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

Abstract

Keywords

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