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Fluctuations of the overlap of the spherical SK model at low temperature Landon, Benjamin


We consider the fluctuations of the overlap between two replicas in the 2-spin spherical SK model in the low temperature phase. We show that the fluctuations are of order $N^{-1/3}$ and are given by a simple, explicit function of the eigenvalues of a GOE matrix. We show that this quantity converges and describe its limit in terms of quantities from random matrix theory. Joint work with P. Sosoe.

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