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We describe the fluctuations of the overlap between two replicas in the2-spin spherical SK model about its limiting value in the low temperaturephase. We show that the fluctuations are of order $N^{-1/3}$ and are given by asimple, explicit function of the eigenvalues of a matrix from the GaussianOrthogonal Ensemble. We show that this quantity converges and describe itslimiting distribution in terms of the Airy1random point field (i.e., the jointlimit of the extremal eigenvalues of the GOE) from random matrix theory.

Fluctuations of the overlap at low temperature in the 2-spin spherical SK model