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Fluctuations of the ground state of the spiked spherical Sherrington-Kirkpatrick model
David Belius, Leon Fröber · 2023-07-27 · via math.PR updates on arXiv.org

The Sherrington-Kirkpatrick Hamiltonian is a random quadratic function on the high-dimensional sphere. This article studies the ground state (i.e. maximum) of this Hamiltonian with external field, or more generally with a non-linear "spike" term. We compute the level of the maximum to leading order, and under appropriate condition its first- and second-order fluctuations. The equivalent results are also derived for the maximum of the model's TAP free energy on the ball.

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