Electronic Journal of Probability
- Electron. J. Probab.
- Volume 18 (2013), paper no. 2, 25 pp.
Central limit theorems for cavity and local fields of the Sherrington-Kirkpatrick model
One of the remarkable applications of the cavity method in the mean field spin glasses is to prove the validity of the Thouless-Anderson-Palmer (TAP) system of equations in the Sherrington-Kirkpatrick (SK) model in the high temperature regime. This naturally leads us to the study of the limit laws for cavity and local fields. The first quantitative results for both fields were obtained by Chatterjee using Stein's method. In this paper, we approach these problems using the Gaussian interpolation technique and establish central limit theorems for both fields by giving moment estimates of all orders.<br />
Electron. J. Probab., Volume 18 (2013), paper no. 2, 25 pp.
Accepted: 6 January 2013
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
This work is licensed under a Creative Commons Attribution 3.0 License.
Chen, Wei-Kuo. Central limit theorems for cavity and local fields of the Sherrington-Kirkpatrick model. Electron. J. Probab. 18 (2013), paper no. 2, 25 pp. doi:10.1214/EJP.v18-1763. https://projecteuclid.org/euclid.ejp/1465064227