## Electronic Journal of Probability

### The Aizenman-Sims-Starr scheme and Parisi formula for mixed $p$-spin spherical models

Wei-Kuo Chen

#### 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.

#### Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 94, 14 pp.

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

https://projecteuclid.org/euclid.ejp/1465064319

Digital Object Identifier
doi:10.1214/EJP.v18-2580

Mathematical Reviews number (MathSciNet)
MR3126577

Zentralblatt MATH identifier
1288.60127

Rights

#### Citation

Chen, Wei-Kuo. The Aizenman-Sims-Starr scheme and Parisi formula for mixed $p$-spin spherical models. Electron. J. Probab. 18 (2013), paper no. 94, 14 pp. doi:10.1214/EJP.v18-2580. https://projecteuclid.org/euclid.ejp/1465064319

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