The number of saddles of the spherical p-spin model

Antonio Auffinger*, Julian Gold

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

MSC Codes 60F10, 82D30.

Original languageEnglish (US)
JournalUnknown Journal
StatePublished - Jul 17 2020


  • Complexity
  • Kac-Rice
  • Number of saddles
  • Spherical p-spin
  • Spin glass

ASJC Scopus subject areas

  • General

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