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arXiv · 2505.02814

Characterization of Gaussian Tensor Ensembles

Rémi Bonnin
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Abstract

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.

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Rémi Bonnin. 2025-05-05. Characterization of Gaussian Tensor Ensembles. https://doi.org/10.3842/sigma.2026.031

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