On the determinant in Bray-Moore's TAP complexity formula
Probability
2024-01-17 v1 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.2401.08529,
title = {On the determinant in Bray-Moore's TAP complexity formula},
author = {David Belius and Francesco Concetti and Giuseppe Genovese},
journal= {arXiv preprint arXiv:2401.08529},
year = {2024}
}