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arXiv · 1906.08471

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

Jean-Christophe Mourrat
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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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Jean-Christophe Mourrat. 2019-06-20. Parisi's formula is a Hamilton-Jacobi equation in Wasserstein space. https://arxiv.org/abs/1906.08471

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