Limit joint distributions of SYK Models with partial interactions, Mixed q-Gaussian Models and Asymptotic $\varepsilon$-freeness
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908938624040960 |
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| author | Liu, Weihua Shen, Haoqi |
| author_facet | Liu, Weihua Shen, Haoqi |
| contents | We study the joint distribution of SYK Hamiltonians for different systems with specified overlaps. We show that, in the large-system limit, their joint distribution converges in distribution to a mixed $q$-Gaussian system. We explain that the graph product of diffusive abelian von Neumann algebras is isomorphic to a $W^*$-probability space generated by the corresponding $\varepsilon$-freely independent random variables with semicircular laws which form a special case of mixed $q$-Gaussian systems that can be approximated by our SYK Hamiltonian models. Thus, we obtain a random model for asymptotic $\varepsilon$-freeness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00789 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Limit joint distributions of SYK Models with partial interactions, Mixed q-Gaussian Models and Asymptotic $\varepsilon$-freeness Liu, Weihua Shen, Haoqi Operator Algebras Mathematical Physics Probability We study the joint distribution of SYK Hamiltonians for different systems with specified overlaps. We show that, in the large-system limit, their joint distribution converges in distribution to a mixed $q$-Gaussian system. We explain that the graph product of diffusive abelian von Neumann algebras is isomorphic to a $W^*$-probability space generated by the corresponding $\varepsilon$-freely independent random variables with semicircular laws which form a special case of mixed $q$-Gaussian systems that can be approximated by our SYK Hamiltonian models. Thus, we obtain a random model for asymptotic $\varepsilon$-freeness. |
| title | Limit joint distributions of SYK Models with partial interactions, Mixed q-Gaussian Models and Asymptotic $\varepsilon$-freeness |
| topic | Operator Algebras Mathematical Physics Probability |
| url | https://arxiv.org/abs/2602.00789 |