| Title: |
A note on outlier eigenvectors for sparse non-Hermitian perturbations |
| Authors: |
Galanis, Miltiadis; Louvaris, Michail |
| Publication Year: |
2026 |
| Collection: |
ArXiv.org (Cornell University Library) |
| Subject Terms: |
Probability; Statistics Theory; 60B20; 15B52 |
| Description: |
We consider a sparse i.i.d.\ non-Hermitian random matrix model $X_n$ (with sparsity parameter $K_n$) and a deterministic finite-rank perturbation $E_n$. Assuming biorthogonality for $E_n$ and a growth condition on $K_n$, we outline a finite-rank resolvent reduction leading to asymptotics for the overlap between an outlier eigenvector of $Y_n:=X_n+E_n$ and the corresponding spike eigenspace. In particular, for an outlier spike $μ$ with $|μ|>1$, the squared projection of the associated (right) eigenvector onto the spike eigenspace converges in probability to $1-|μ|^{-2}$. Our result generalizes Theorem 1.6 of [HLN26] to general finite rank case solving Open Problem 5. ; 10 pages |
| Document Type: |
text |
| Language: |
unknown |
| Relation: |
http://arxiv.org/abs/2603.03972 |
| Availability: |
http://arxiv.org/abs/2603.03972 |
| Accession Number: |
edsbas.299D0D67 |
| Database: |
BASE |