Corpus ID: 235458169

Noise sensitivity for the top eigenvector of a sparse random matrix

@inproceedings{Bordenave2021NoiseSF,
  title={Noise sensitivity for the top eigenvector of a sparse random matrix},
  author={C. Bordenave and Jaehun Lee},
  year={2021}
}
We investigate the noise sensitivity of the top eigenvector of a sparse random symmetric matrix. Let v be the top eigenvector of an N × N sparse random symmetric matrix with an average of d nonzero centered entries per row. We resample k randomly chosen entries of the matrix and obtain another realization of the random matrix with top eigenvector v. Building on recent results on sparse random matrices and a noise sensitivity analysis previously developed for Wigner matrices, we prove that, if d… Expand
Higher order fluctuations of extremal eigenvalues of sparse random matrices
  • Jaehun Lee
  • Mathematics
  • 2021
We study higher-order fluctuations of extremal eigenvalues of sparse random matrices on the regime Nǫ ≪ q ≪ N1/2 where q is the sparsity parameter. In the case N1/9 ≪ q ≪ N1/6, it was known thatExpand

References

SHOWING 1-10 OF 26 REFERENCES
Eigenvector Statistics of Sparse Random Matrices
We prove that the bulk eigenvectors of sparse random matrices, i.e. the adjacency matrices of Erdős-Renyi graphs or random regular graphs, are asymptotically jointly normal, provided the averagedExpand
Local law and Tracy–Widom limit for sparse random matrices
We consider spectral properties and the edge universality of sparse random matrices, the class of random matrices that includes the adjacency matrices of the Erdős–Rényi graph model G(N, p). We proveExpand
Tail bounds for gaps between eigenvalues of sparse random matrices
We prove the first eigenvalue repulsion bound for sparse random matrices. As a consequence, we show that these matrices have simple spectrum, improving the range of sparsity and error probabilityExpand
Noise sensitivity of the top eigenvector of a Wigner matrix
We investigate the noise sensitivity of the top eigenvector of a Wigner matrix in the following sense. Let v be the top eigenvector of an $$N\times N$$ N × N Wigner matrix. Suppose that k randomlyExpand
Spectral Statistics of Erdős-Rényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues
We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs, i.e. graphs on N vertices where every edge is chosen independently and with probability p ≡ p(N). We rescale the matrix soExpand
No-gaps delocalization for general random matrices
We prove that with high probability, every eigenvector of a random matrix is delocalized in the sense that any subset of its coordinates carries a non-negligible portion of its $${\ell_2}$$ℓ2 norm.Expand
Largest eigenvalues of sparse inhomogeneous Erdős–Rényi graphs
We consider inhomogeneous Erd\H{o}s-R\'enyi graphs. We suppose that the maximal mean degree $d$ satisfies $d \ll \log n$. We characterize the asymptotic behavior of the $n^{1 - o(1)}$ largestExpand
Spectral statistics of Erdős–Rényi graphs I: Local semicircle law
We consider the ensemble of adjacency matrices of Erdős–Renyi random graphs, that is, graphs on N vertices where every edge is chosen independently and with probability p≡p(N). We rescale the matrixExpand
Fluctuations of extreme eigenvalues of sparse Erdős–Rényi graphs
We consider a class of sparse random matrices which includes the adjacency matrix of the Erdős-Renyi graph $\mathcal{G}(N,p)$. We show that if $N^{\varepsilon} \leq Np \leq N^{1/3-\varepsilon}$ thenExpand
Universality of Sine-Kernel for Wigner Matrices with a Small Gaussian Perturbation
We consider $N\times N$ Hermitian random matrices with independent identically distributed entries (Wigner matrices). We assume that the distribution of the entries have a Gaussian component withExpand
...
1
2
3
...