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PreprintCC BY 4.0arXiv

Multilevel limits of spiked random matrix corners processes

  • Benjamin Landon
  • Tara Stojimirovic
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Abstract

We consider the largest eigenvalues of submatrices of the classical Gaussian random matrices with a finite rank spike in the critical BBP regime. We show that they converge to a multilevel interlacing particle system whose lowest level is the Airyβ point process. Our construction and scaling limits extend in a natural way to non-classical β>0.

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Cite

BibTeXRIS
BibTeX
@misc{landon2026multilevel,
  title = {{Multilevel limits of spiked random matrix corners processes}},
  author = {Benjamin Landon and Tara Stojimirovic},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.01531},
  eprint = {2608.01531},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.01531},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Multilevel limits of spiked random matrix corners processes
AU  - Benjamin Landon
AU  - Tara Stojimirovic
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2608.01531
UR  - https://arxiv.org/abs/2608.01531
AB  - We consider the largest eigenvalues of submatrices of the classical Gaussian random matrices with a finite rank spike in the critical BBP regime. We show that they converge to a multilevel interlacing particle system whose lowest level is the Airy_β point process. Our construction and scaling limits extend in a natural way to non-classical β>0.
ER  -