Universality of the fluctuations of the free energy in generalized Sherrington-Kirkpatrick models and the log likelihood ratio in spiked Wigner models
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| Format: | Preprint |
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2026
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| _version_ | 1866910247231160320 |
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| author | Choo, Hyunsuk Han, Yoochan Lee, Ji Oon |
| author_facet | Choo, Hyunsuk Han, Yoochan Lee, Ji Oon |
| contents | We consider the fluctuations of the free energy in generalized Sherrington-Kirkpatrick models and the log likelihood ratio of spiked Wigner models in the high temperature/subcritical regime. We prove that the limiting laws of the fluctuations are Gaussian under suitable assumptions, and the result is universal in the sense that it does not depend on the distribution of the disorder or the prior except that the means and the variances of the limiting laws depend on a few parameters of the model. The proof is based on the multigraph expansion that provides a unified approach to analyze both models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_07050 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Universality of the fluctuations of the free energy in generalized Sherrington-Kirkpatrick models and the log likelihood ratio in spiked Wigner models Choo, Hyunsuk Han, Yoochan Lee, Ji Oon Probability Mathematical Physics Statistics Theory 82B44, 60F05, 62H15 We consider the fluctuations of the free energy in generalized Sherrington-Kirkpatrick models and the log likelihood ratio of spiked Wigner models in the high temperature/subcritical regime. We prove that the limiting laws of the fluctuations are Gaussian under suitable assumptions, and the result is universal in the sense that it does not depend on the distribution of the disorder or the prior except that the means and the variances of the limiting laws depend on a few parameters of the model. The proof is based on the multigraph expansion that provides a unified approach to analyze both models. |
| title | Universality of the fluctuations of the free energy in generalized Sherrington-Kirkpatrick models and the log likelihood ratio in spiked Wigner models |
| topic | Probability Mathematical Physics Statistics Theory 82B44, 60F05, 62H15 |
| url | https://arxiv.org/abs/2605.07050 |