Central Limit Theorems for the Energy Density in?the?Sherrington-Kirkpatrick Model |
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Authors: | Sourav Chatterjee and Nicholas Crawford |
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Abstract: | In this paper we consider central limit theorems for various macroscopic observables in the high temperature region of the
Sherrington-Kirkpatrick spin glass model. With a particular focus on obtaining a quenched central limit theorem for the energy
density of the system with non-zero external field, we show how to combine the mean field cavity method with Stein’s method
in the quenched regime. The result for the energy density extends the corresponding result of Comets and Neveu in the case
of zero external field. |
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