Outliers in the spectrum of iid matrices with bounded rank perturbations

Details Outliers in the spectrum of iid matrices with bounded rank perturbations Outliers in the spectrum of iid matrices with bounded rank perturbations

2010-12-21

arxiv.org/abs/1012.4818v4

Mathematics

Probability

24 pages, 5 figures, to appear, Prob. Thy. and Related Fields. This is the final version, incorporating the referee comments

Scientific paper

It is known that if one perturbs a large iid random matrix by a bounded rank error, then the majority of the eigenvalues will remain distributed according to the circular law. However, the bounded rank perturbation may also create one or more outlier eigenvalues. We show that if the perturbation is small, then the outlier eigenvalues are created next to the outlier eigenvalues of the bounded rank perturbation; but if the perturbation is large, then many more outliers can be created, and their law is governed by the zeroes of a random Laurent series with Gaussian coefficients. On the other hand, these outliers may be eliminated by enforcing a row sum condition on the final matrix.

Affiliated with

Also associated with

No associations

Rating

Outliers in the spectrum of iid matrices with bounded rank perturbations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Outliers in the spectrum of iid matrices with bounded rank perturbations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Outliers in the spectrum of iid matrices with bounded rank perturbations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-581078