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Pré-Publication, Document De Travail Année : 2023

Un-inverting the Parisi formula

Résumé

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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Dates et versions

hal-04232501 , version 1 (08-10-2023)

Identifiants

Citer

Jean-Christophe Mourrat. Un-inverting the Parisi formula. 2023. ⟨hal-04232501⟩
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