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2013 The Aizenman-Sims-Starr scheme and Parisi formula for mixed $p$-spin spherical models
Wei-Kuo Chen
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Electron. J. Probab. 18: 1-14 (2013). DOI: 10.1214/EJP.v18-2580

Abstract

The Parisi formula for the free energy in the spherical models with mixed even $p$-spin interactions was proven in Michel Talagrand. In this paper we study the general mixed $p$-spin spherical models including $p$-spin interactions for odd $p$. We establish the Aizenman Sims-Starr scheme and from this together with many well-known results and Dmitry Panchenko's recent proof on the Parisi ultrametricity conjecture, we prove the Parisi formula.

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Wei-Kuo Chen. "The Aizenman-Sims-Starr scheme and Parisi formula for mixed $p$-spin spherical models." Electron. J. Probab. 18 1 - 14, 2013. https://doi.org/10.1214/EJP.v18-2580

Information

Accepted: 29 October 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1288.60127
MathSciNet: MR3126577
Digital Object Identifier: 10.1214/EJP.v18-2580

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