On the determinant in Bray-Moore's TAP complexity formula
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913198201896960 |
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| author | Belius, David Concetti, Francesco Genovese, Giuseppe |
| author_facet | Belius, David Concetti, Francesco Genovese, Giuseppe |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08529 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the determinant in Bray-Moore's TAP complexity formula Belius, David Concetti, Francesco Genovese, Giuseppe Probability Mathematical Physics 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. |
| title | On the determinant in Bray-Moore's TAP complexity formula |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2401.08529 |