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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.15377 |
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| _version_ | 1866918157290045440 |
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| author | Franchini, Simone |
| author_facet | Franchini, Simone |
| contents | We discuss the relation between p-adic numbers and kernels in view of a recent large deviation theory for mean-field spin glasses. As an application we show several fundamental properties of numerical bases in kernel language. In particular, we show that the Derrida's Generalized Random Energy Model can be interpreted as a (random) numerical base. We also show an application to the Primon gas and the Riemann Zeta Function by constructing a kernel representation of the Primon gas based on a finite p-base, thereby establishing a concrete link between number theory and kernel theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15377 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | P-adic numbers and kernels Franchini, Simone Disordered Systems and Neural Networks Statistical Mechanics 11Z05 G.2.1 We discuss the relation between p-adic numbers and kernels in view of a recent large deviation theory for mean-field spin glasses. As an application we show several fundamental properties of numerical bases in kernel language. In particular, we show that the Derrida's Generalized Random Energy Model can be interpreted as a (random) numerical base. We also show an application to the Primon gas and the Riemann Zeta Function by constructing a kernel representation of the Primon gas based on a finite p-base, thereby establishing a concrete link between number theory and kernel theory. |
| title | P-adic numbers and kernels |
| topic | Disordered Systems and Neural Networks Statistical Mechanics 11Z05 G.2.1 |
| url | https://arxiv.org/abs/2411.15377 |