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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | https://arxiv.org/abs/2601.16099 |
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| _version_ | 1866912961004568576 |
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| author | Maeta, Reishi |
| author_facet | Maeta, Reishi |
| contents | We propose a bootstrap approximation method for the Hermitian one-matrix model that does not rely on positivity constraints. The theoretical foundation of this method is that the one-matrix model admits an eigenvalue distribution $ρ(λ)$, and that the moments $w_n$ generated from it satisfy the loop equations. Our framework is designed to numerically determine a self-consistent pair of $ρ(λ)$ and $w_n$ that simultaneously satisfies these two requirements. In the concrete implementation the least-squares method is employed, and since the sign problem is absent in this formulation, the method can be formally applied to the Minkowski one-matrix model as well, provided that the one-cut structure of the resolvent is assumed. Actual numerical calculations show that this bootstrap approximation reproduces, with very high accuracy, the exact solutions for Euclidean-type models and the perturbative results for Minkowski-type models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16099 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Matrix Bootstrap Approximation without Positivity Constraint Maeta, Reishi High Energy Physics - Theory We propose a bootstrap approximation method for the Hermitian one-matrix model that does not rely on positivity constraints. The theoretical foundation of this method is that the one-matrix model admits an eigenvalue distribution $ρ(λ)$, and that the moments $w_n$ generated from it satisfy the loop equations. Our framework is designed to numerically determine a self-consistent pair of $ρ(λ)$ and $w_n$ that simultaneously satisfies these two requirements. In the concrete implementation the least-squares method is employed, and since the sign problem is absent in this formulation, the method can be formally applied to the Minkowski one-matrix model as well, provided that the one-cut structure of the resolvent is assumed. Actual numerical calculations show that this bootstrap approximation reproduces, with very high accuracy, the exact solutions for Euclidean-type models and the perturbative results for Minkowski-type models. |
| title | Matrix Bootstrap Approximation without Positivity Constraint |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.16099 |