• Corpus ID: 245650713

Rank $1$ perturbations in random matrix theory -- a review of exact results

  title={Rank \$1\$ perturbations in random matrix theory -- a review of exact results},
  author={Peter J. Forrester},
A number of random matrix ensembles permitting exact determination of their eigenvalue and eigenvector statistics maintain this property under a rank 1 perturbation. Considered in this review are the additive rank 1 perturbation of the Hermitian Gaussian ensembles, the multiplicative rank 1 perturbation of the Wishart ensembles, and rank 1 perturbations of Hermitian and unitary matrices giving rise to a two-dimensional support for the eigenvalues. The focus throughout is on exact formulas… 
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