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

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES（2022）

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摘要

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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关键词

Spin glass, Hamilton-Jacobi equation, Wasserstein space

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