Electronic Journal of Probability

Central limit theorems for cavity and local fields of the Sherrington-Kirkpatrick model

Wei-Kuo Chen

Full-text: Open access

Abstract

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 />

Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 2, 25 pp.

Dates
Accepted: 6 January 2013
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465064227

Digital Object Identifier
doi:10.1214/EJP.v18-1763

Mathematical Reviews number (MathSciNet)
MR3024096

Zentralblatt MATH identifier
1288.60126

Subjects
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.)

Keywords
Sherrington-Kirkpatrick model Stein's method TAP equations

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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


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References

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