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arXiv · 2308.10715

Un-inverting the Parisi formula

Jean-Christophe Mourrat
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Abstract

The free energy of any system can be written as the supremum of a functional involving an energy term and an entropy term. Surprisingly, the limit free energy of mean-field spin glasses is expressed as an infimum instead, a phenomenon sometimes called an inverted variational principle. Using a stochastic-control representation of the Parisi functional and convex duality arguments, we rewrite this limit free energy as a supremum over martingales in a Wiener space.

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Jean-Christophe Mourrat. 2023-08-21. Un-inverting the Parisi formula. https://arxiv.org/abs/2308.10715

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