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Abstract: We introduce some applications of Stein-s method in the high temperatureanalysis of spin glasses. Stein-s method allows the direct analysis of theGibbs measure without having to create a cavity. Another advantage is that itgives limit theorems with total variation error bounds, although the bounds canbe suboptimal. A surprising byproduct of our analysis is a relativelytransparent explanation of the Thouless-Anderson-Palmer system of equations.Along the way, we develop Stein-s method for mixtures of two Gaussiandensities.

Author: Sourav Chatterjee

Source: https://arxiv.org/

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