Haut PDF Eigenvalues and eigenvectors of large matrices under random perturbations
Eigenvalues and eigenvectors of large matrices under random perturbations
... theory of the spectrum of random matrices emerged through the work [ Wig55 ] of Nobel Prize winner Eugene ...context of his physical studies of heavy nuclei, the behavior ...
108
The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
... words and phrases. Random matrices, Haar measure, principal components analysis, informa- tional limit, free probability, phase transition, random eigenvalues, random ...
28
A Subspace Estimator for Fixed Rank Perturbations of Large Random Matrices
... problem of parameter estimation based on certain eigenspaces of the empirical covariance matrix of an observed multidimensional time series, in the case where the time series dimension and the ...
28
On the outlying eigenvalues of a polynomial in large independent random matrices
... the eigenvectors associated to these outlying eigenvalues have projections of computable size onto the eigenspaces of A N corresponding to the ...6.1 and 6.3. Sections 4 and 5 ...
38
Kernel random matrices of large concentrated data: the example of GAN-generated images
... (b) and (c) for the generated images, and even for real images in (e) and ...spikes and the almost perfect match between the corre- sponding eigenvectors, which provide clustering ...
6
A Survey on the Eigenvalues Local Behavior of Large Complex Correlated Wishart Matrices
... entries of matrix X N are complex Gaussian. It is however of major interest, for applications and for the general theory as well, to study the universality of such results for non-Gaussian ...
30
On bilinear forms based on the resolvent of large random matrices
... analogues of the type ˜ u n Q ˜ n (z)˜ v ∗ n can be circumvented to establish first order results for non-centered random matrices (see for in- stance [8], ...behavior of individual entries ...
36
A CLT for linear spectral statistics of large random information-plus-noise matrices
... lack of convergence lies in the fact that these additional terms not only depend on the spectrum of A n A ∗ n , but also on the spectrum of A n A T n and on A n A ∗ n ’s ...convergence ...
23
Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices
... Most of the spectrum of a large matrix is not much altered if one adds a finite rank perturbation to the matrix, simply because of Weyl’s interlacement properties of the ...extreme ...
41
Isolated eigenvalues of non Hermitian random matrices
... a large matrix barely changes the global behavior of its ...some of the eigenvalues, called outliers, can deviate away from the bulk of the spectrum, depending on the strength of ...
161
Large deviations of the extreme eigenvalues of random deformations of matrices
... RANDOM DEFORMATIONS OF MATRICES ...n of size n with spectral measure converging to a compactly supported probability ...a random finite rank matrix, with delocalized ...law of ...
45
Eigenvalues of Euclidean Random Matrices
... remainder of this paper is organized as ...3 and Proposition ...the eigenvectors of A and on the correlation of the ...(x)| and B(x, r) will denote the open ball of ...
25
Characterization of Random Matrix Eigenvectors for Stochastic Block Model
... NTRODUCTION Large graphs have become an important area of research in recent times, owing to burgeoning interest in the analysis of Facebook™ , Twitter™ and other social ...host of ...
6
Dynamics of eigenvectors of random matrices and eigenvalues of nonlinear models of matrices
... study of large interacting quantum systems, Wigner conjectured that empirical results are well approximated by statistics of eigenvalues of large random ...overview ...
162
Probability density of determinants of random matrices
... if and only if Ax = 0 has a non-zero solution x 6= 0, (ii) det(AB) = det ...rows of A. So the definition of a determinant varies according to which of the property or properties one wants to ...
11
Outlier eigenvalues for non-Hermitian polynomials in independent i.i.d. matrices and deterministic matrices
... conclusion of our lemma. As noted before, u is a vector of zeros and ...construction of L that the number of ones is dominated by the number of monomials of P , quantity ...
51
Eigenvalues and Spectral Dimension of Random Geometric Graphs in Thermodynamic Regime
... properties of suitably defined Laplacian ...spectrum of the normal- ized Laplacian matrix. However, to overcome the problem of singularities due to iso- lated vertices in the termodynamic regime, we ...
11
Large deviations for the Boussinesq Equations under Random Influences
... UNDER RANDOM INFLUENCES JINQIAO DUAN AND ANNIE MILLET ...convection under random influ- ences is considered as a system of stochastic partial differential ...system of ...
32
Large deviations for the largest eigenvalue of the sum of two random matrices
... spectrum of the sum A + B of two Hermitian matrices know- ing the spectra of A and B respectively is a classical and difficult ...works of Voiculescu [ 1991 ], we know that ...
21
Random matrices and the Potts model on random graphs
... Random matrices and the Potts model on random graphs Alice Guionnet Abstract These are the lecture notes for a mini-course given in ...Probability and Statistical Physics during June ...
34
