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PreprintCC BY 4.0arXiv

Random waves on sub-Riemannian SU(2)

  • Marco Carfagnini
  • Karwan Angulugaha Gamage
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Abstract

Random spherical eigenfunctions for the Lalplace-Beltrami operator are well understood and their local behavior, after renormalization, is described by Berry's random wave model. In this paper we construct a family of random fields on the sphere 𝕊3, identified with the group SU(2), endowed with a sub-Riemannian structure. These fields are random eigenfunctions for the sub-Laplacian and they are constructed from matrix elements of unitary irreducible representations of SU(2). We prove that the local behavior of such fields is the same as the Berry-Heisenberg random field on the Heisenberg group introduced in [10].

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Cite

BibTeXRIS
BibTeX
@misc{carfagnini2026random,
  title = {{Random waves on sub-Riemannian $SU(2)$}},
  author = {Marco Carfagnini and Karwan Angulugaha Gamage},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06218},
  eprint = {2611.06218},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06218},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Random waves on sub-Riemannian SU(2)
AU  - Marco Carfagnini
AU  - Karwan Angulugaha Gamage
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06218
UR  - https://arxiv.org/abs/2611.06218
AB  - Random spherical eigenfunctions for the Lalplace-Beltrami operator are well understood and their local behavior, after renormalization, is described by Berry's random wave model. In this paper we construct a family of random fields on the sphere 𝕊^3, identified with the group SU(2), endowed with a sub-Riemannian structure. These fields are random eigenfunctions for the sub-Laplacian and they are constructed from matrix elements of unitary irreducible representations of SU(2). We prove that the local behavior of such fields is the same as the Berry-Heisenberg random field on the Heisenberg group introduced in [10].
ER  -