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PreprintCC BY 4.0arXiv

Joint distributions of eigenvectors of symmetric random tensors

  • Naoki Sasakura
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Abstract

We compute the joint distributions of arbitrary numbers of eigenvectors of real and complex symmetric random tensors by the quantum field theoretical methods which were previously used to compute the mean distributions. We obtain the random matrix representations and the large-dimension asymptotics of the joint distributions. The latter can be expressed by a common function of tensor geometries, extending the universality found for the mean distributions to the joint distributions. Several crosschecks of our results are carried out by Monte Carlo computations.

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Cite

BibTeXRIS
BibTeX
@misc{sasakura2026joint,
  title = {{Joint distributions of eigenvectors of symmetric random tensors}},
  author = {Naoki Sasakura},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.09804},
  eprint = {2605.09804},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.09804},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Joint distributions of eigenvectors of symmetric random tensors
AU  - Naoki Sasakura
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2605.09804
UR  - https://arxiv.org/abs/2605.09804
AB  - We compute the joint distributions of arbitrary numbers of eigenvectors of real and complex symmetric random tensors by the quantum field theoretical methods which were previously used to compute the mean distributions. We obtain the random matrix representations and the large-dimension asymptotics of the joint distributions. The latter can be expressed by a common function of tensor geometries, extending the universality found for the mean distributions to the joint distributions. Several crosschecks of our results are carried out by Monte Carlo computations.
ER  -