Central Limit Theorems for the Energy Density in the Sherrington-Kirkpatrick Model

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-Neveu.

30 pages Mild Update:typos, referee comments regarding terminology

References in corpus (5)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• The Thermodynamic Limit in Mean Field Spin Glass Models
• An Extended Variational Principle for the SK Spin-Glass Model
• The infinite volume limit in generalized mean field disordered models
• Cavity method in the spherical Sherrington-Kirkpatrick model