Weingarten calculus for centered random permutation matrices
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866914546746130432 |
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| author | Collins, Benoît Nagatsu, Manasa |
| author_facet | Collins, Benoît Nagatsu, Manasa |
| contents | We introduce and study the Weingarten calculus for centered random permutation matrices in the symmetric group S_N. After presenting a formulation of the Weingarten calculus on the symmetric group, we derive a formula in the centered case, as well as a sign-respecting formula. Our investigations uncover the fact that a building block of this Weingarten calculus is Kummer's confluent hypergeometric function. It allows us to derive multiple algebraic properties of the Weingarten function and uniform estimate. These results shed a conceptual light on phenomena that take place regarding the algebraic and asymptotic behavior of moments of random permutations in the resolution of Bordenave and Bordenave-Collins of strong convergence. We obtain multiple new non-trivial estimates for moments of coefficients in centered moments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18453 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weingarten calculus for centered random permutation matrices Collins, Benoît Nagatsu, Manasa Probability Combinatorics 28C10, 15B52 We introduce and study the Weingarten calculus for centered random permutation matrices in the symmetric group S_N. After presenting a formulation of the Weingarten calculus on the symmetric group, we derive a formula in the centered case, as well as a sign-respecting formula. Our investigations uncover the fact that a building block of this Weingarten calculus is Kummer's confluent hypergeometric function. It allows us to derive multiple algebraic properties of the Weingarten function and uniform estimate. These results shed a conceptual light on phenomena that take place regarding the algebraic and asymptotic behavior of moments of random permutations in the resolution of Bordenave and Bordenave-Collins of strong convergence. We obtain multiple new non-trivial estimates for moments of coefficients in centered moments. |
| title | Weingarten calculus for centered random permutation matrices |
| topic | Probability Combinatorics 28C10, 15B52 |
| url | https://arxiv.org/abs/2503.18453 |