Extending the Parisi formula along a Hamilton-Jacobi equation
| Autor: | Mourrat, Jean-Christophe, Panchenko, Dmitry |
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| Rok vydání: | 2019 |
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| Zdroj: | Electron. J. Probab. 25 (23), 1-17 (2020) |
| Druh dokumentu: | Working Paper |
| Popis: | 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 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. Comment: 16 pages |
| Databáze: | arXiv |
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