Regularization of Non-Normal Matrices by Gaussian Noise

Ohad Noy Feldheim, Elliot Paquette*, Ofer Zeitouni

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We consider the regularization of matrices MN in Jordan form by additive Gaussian noise N{-\gamma }GN, where GN is a matrix of i.i.d. standard Gaussians and \gamma >{\tfrac {1}{2}} so that the operator norm of the additive noise tends to 0 with N. Under mild conditions on the structure of MN, we evaluate the limit of the empirical measure of eigenvalues of MN+N{-\gamma } GN and show that it depends on \gamma, in contrast with the case of a single Jordan block.

Original languageAmerican English
Pages (from-to)8724-8751
Number of pages28
JournalInternational Mathematics Research Notices
Issue number18
StatePublished - 2015
Externally publishedYes

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