A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf
.
Overlaps, Eigenvalue Gaps, and Pseudospectrum under real Ginibre and Absolutely Continuous Perturbations
[article]
2020
arXiv
pre-print
Let G_n be an n × n matrix with real i.i.d. N(0,1/n) entries, let A be a real n × n matrix with ‖ A ‖< 1, and let γ∈ (0,1). We show that with probability 0.99, A + γ G_n has all of its eigenvalue condition numbers bounded by O(n^5/2/γ^3/2) and eigenvector condition number bounded by O(n^3 /γ^3/2). Furthermore, we show that for any s > 0, the probability that A + γ G_n has two eigenvalues within distance at most s of each other is O(n^4 s^1/3/γ^5/2). In fact, we show the above statements hold in
arXiv:2005.08930v1
fatcat:ocuftxwhnfc3xlar3gepgndi7e