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Multiplicative non-Hermitian perturbations of classical $\beta$-ensembles

Probability 2025-12-29 v2 Mathematical Physics math.MP

Abstract

We compute the joint eigenvalue distribution for a multiplicative non-Hermitian perturbation (I+iΓ)H(I+i\Gamma)H, rankΓ=1\operatorname{rank}\,\Gamma=1 of a random matrix HH from the Gaussian, Laguerre, and chiral Gaussian β\beta-ensembles.

Keywords

Cite

@article{arxiv.2308.06627,
  title  = {Multiplicative non-Hermitian perturbations of classical $\beta$-ensembles},
  author = {Gökalp Alpan and Rostyslav Kozhan},
  journal= {arXiv preprint arXiv:2308.06627},
  year   = {2025}
}

Comments

Some improvements over the previous version