Geodesic
The Parisi formula is a Hamilton–Jacobi equation in Wasserstein space
Canadian journal of mathematics, Tome 74 (2022) no. 3, pp. 607-629

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DOI

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.
DOI : 10.4153/S0008414X21000031
Mots-clés : Spin glass, Hamilton–Jacobi equation, Wasserstein space 
Mourrat, Jean-Christophe. The Parisi formula is a Hamilton–Jacobi equation in Wasserstein space. Canadian journal of mathematics, Tome 74 (2022) no. 3, pp. 607-629. doi: 10.4153/S0008414X21000031
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     title = {The {Parisi} formula is a {Hamilton{\textendash}Jacobi} equation in {Wasserstein} space},
     journal = {Canadian journal of mathematics},
     pages = {607--629},
     year = {2022},
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     doi = {10.4153/S0008414X21000031},
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