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2020 Extending the Parisi formula along a Hamilton-Jacobi equation
Jean-Christophe Mourrat, Dmitry Panchenko
Electron. J. Probab. 25: 1-17 (2020). DOI: 10.1214/20-EJP432

Abstract

We study the free energy of mixed $p$-spin spin glass models enriched with an additional magnetic field given by the canonical Gaussian field associated with a Ruelle probability cascade. We prove the conjecture in [15] that this free energy converges to the Hopf-Lax solution of a certain Hamilton-Jacobi equation. Using this result, we give a new representation of the free energy of mixed $p$-spin models with soft spins.

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Jean-Christophe Mourrat. Dmitry Panchenko. "Extending the Parisi formula along a Hamilton-Jacobi equation." Electron. J. Probab. 25 1 - 17, 2020. https://doi.org/10.1214/20-EJP432

Information

Received: 1 November 2019; Accepted: 8 February 2020; Published: 2020
First available in Project Euclid: 15 February 2020

zbMATH: 1439.82019
MathSciNet: MR4073684
Digital Object Identifier: 10.1214/20-EJP432

Subjects:
Primary: 82B44, 82D30

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