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On the determinant in Bray-Moore's TAP complexity formula

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arxiv 2401.08529 v1 pith:DKBQZZUY submitted 2024-01-16 math.PR math-phmath.MP

David Belius , Francesco Concetti , Giuseppe Genovese This is my paper · ORCID
classification math.PRmath-phmath.MP
keywords complexitydeterminantbraycomputationformulamoorebehaviourbray-moore
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In the computation of the TAP complexity, originally carried out by Bray and Moore, a fundamental step is to calculate the determinant of a random Hessian. As the replica method does not give a clear prescription, physicists debated how to perform this computation and its consequences on the TAP complexity for a long time. In this paper we prove the original Bray and Moore formula for the behaviour of the determinant at exponential scale to be correct, and compute an important prefactor coming from a small outlier in the spectrum.

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  1. Large deviations for the maximum of the generalized TAP free energy

    math.PR 2026-07 conditional novelty 7.0 of 10

    The large-deviation exponent for existence of TAP maxima equals the Legendre transform of a constrained Parisi value, not the ordinary annealed complexity.

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