Characterization of Gaussian Tensor Ensembles
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908927183028224 |
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| author | Bonnin, Rémi |
| author_facet | Bonnin, Rémi |
| contents | The starting point of this work is a theorem due to Maxwell characterizing the distribution of a Gaussian vector with at least two coordinates. We define the Gaussian orthogonal, unitary and symplectic tensor ensembles for notions of real symmetric, hermitian and self-dual hermitian tensors which recover the classical vector and matrix Gaussian ensembles when the order is one and two. We give a complete family of invariant polynomials for orthogonal, unitary and symplectic transformations and we prove a Maxwell-type theorem for these Gaussian tensor distributions unifying and extending the ones known for vectors and matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02814 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterization of Gaussian Tensor Ensembles Bonnin, Rémi Mathematical Physics Probability The starting point of this work is a theorem due to Maxwell characterizing the distribution of a Gaussian vector with at least two coordinates. We define the Gaussian orthogonal, unitary and symplectic tensor ensembles for notions of real symmetric, hermitian and self-dual hermitian tensors which recover the classical vector and matrix Gaussian ensembles when the order is one and two. We give a complete family of invariant polynomials for orthogonal, unitary and symplectic transformations and we prove a Maxwell-type theorem for these Gaussian tensor distributions unifying and extending the ones known for vectors and matrices. |
| title | Characterization of Gaussian Tensor Ensembles |
| topic | Mathematical Physics Probability |
| url | https://arxiv.org/abs/2505.02814 |