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PreprintarXiv licencearXiv

R-transforms for non-Hermitian block random matrices: a spherical integral approach

  • Pierre Bousseyroux
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Abstract

We extend the spherical-integral approach to ℛ-transforms of non-Hermitian random matrices to random matrices with a fixed K × K block structure. We introduce a rank-K spherical integral defining a scalar H-transform on 2K × 2K overlap matrices and an associated matrix-valued ℛ-transform encoding the joint block structure. Using the replica method, we derive a conjectural subordination relation for sums of independent block matrices. This framework provides a method for determining the spectral boundaries of large non-Hermitian random matrices with a fixed block structure.

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Cite

BibTeXRIS
BibTeX
@misc{bousseyroux2026rtransforms,
  title = {{R-transforms for non-Hermitian block random matrices: a spherical integral approach}},
  author = {Pierre Bousseyroux},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31730},
  eprint = {2609.31730},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31730},
}
RIS
TY  - UNPB
TI  - R-transforms for non-Hermitian block random matrices: a spherical integral approach
AU  - Pierre Bousseyroux
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.31730
UR  - https://arxiv.org/abs/2609.31730
AB  - We extend the spherical-integral approach to ℛ-transforms of non-Hermitian random matrices to random matrices with a fixed K × K block structure. We introduce a rank-K spherical integral defining a scalar H-transform on 2K × 2K overlap matrices and an associated matrix-valued ℛ-transform encoding the joint block structure. Using the replica method, we derive a conjectural subordination relation for sums of independent block matrices. This framework provides a method for determining the spectral boundaries of large non-Hermitian random matrices with a fixed block structure.
ER  -