The number of saddles of the spherical p-spin model

2020/07/17 by Antonio Auffinger, Auffinger, Antonio, Julian Gold +1
Mathematics · Physics and Astronomy · #60F10 #82D30 #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2007.09269

openalex publication_date 2020/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

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