Regularization of Non-Normal Matrices by Gaussian Noise

Ohad Noy Feldheim; Elliot Paquette; Ofer Zeitouni

doi:10.1093/imrn/rnu213

Regularization of Non-Normal Matrices by Gaussian Noise

Ohad Noy Feldheim, Elliot Paquette^*, Ofer Zeitouni

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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Abstract

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 language	English
Pages (from-to)	8724-8751
Number of pages	28
Journal	International Mathematics Research Notices
Volume	2015
Issue number	18
DOIs	https://doi.org/10.1093/imrn/rnu213
State	Published - 2015
Externally published	Yes

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Regularization of Non-Normal Matrices by Gaussian Noise

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