Spin glasses and Stein's method

• 成果类型: Article
• 署名作者: Chatterjee, Sourav
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-009-0240-8
• 发表日期: 2010
• 页码: 567-600
• 关键词: sherrington-kirkpatrick model; stochastic calculus; solvable model; field; approximation; clt

摘要

We introduce some applications of Stein's method in the high temperature analysis of spin glasses. Stein's method allows the direct analysis of the Gibbs measure without having to eate a cavity. Another advantage is that it gives limit theorems with total variation error bounds, although the bounds can be suboptimal. A surprising byproduct of our analysis is a relatively transparent explanation of the Thouless-Anderson-Palmer system of equations. Along the way, we develop Stein's method for mixtures of two Gaussian densities.