The number of saddles of the spherical $p$-spin model

Antonio Auffinger; Julian Gold

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arXiv · 2007.09269

The number of saddles of the spherical $p$-spin model

Antonio Auffinger·Julian Gold

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Abstract

We show that the quenched complexity of saddles of the spherical pure $p$-spin model agrees with the annealed complexity when both are positive. Precisely, we show that the second moment of the number of critical values of a given finite index in a given interval has twice the growth rate of the first moment.

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Antonio Auffinger, Julian Gold. 2020-07-17. The number of saddles of the spherical $p$-spin model. https://arxiv.org/abs/2007.09269

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