Spin glasses and Stein's method

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Chatterjee, Sourav
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Abstract
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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 create 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.
Comment: 29 pages. Final version. To appear in PTRF
Keywords
Mathematics - Probability, Mathematical Physics, 60K35, 82B44
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