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


 
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1. Title Title of document Central limit theorems for cavity and local fields of the Sherrington-Kirkpatrick model
 
2. Creator Author's name, affiliation, country Wei-Kuo Chen; University of California, Irvine; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Sherrington-Kirkpatrick model; Stein's method; TAP equations
 
3. Subject Subject classification 60K35; 82B44
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
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7. Date (YYYY-MM-DD) 2013-01-06
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/1763
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-1763
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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