# Haut PDF Eigenvalues and eigenvectors of large matrices under random perturbations

### Eigenvalues and eigenvectors of large matrices under random perturbations

**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 ...

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### The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices

**and**phrases.

**Random**

**matrices**, Haar measure, principal components analysis, informa- tional limit, free probability, phase transition,

**random**

**eigenvalues**,

**random**...

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### A Subspace Estimator for Fixed Rank Perturbations of Large Random Matrices

**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 ...

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### On the outlying eigenvalues of a polynomial in large independent random matrices

**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 ...

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### Kernel random matrices of large concentrated data: the example of GAN-generated images

**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

**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 ...

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### On bilinear forms based on the resolvent of large random matrices

**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 ...

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### A CLT for linear spectral statistics of large random information-plus-noise matrices

**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 ...

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### Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices

**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 ...

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### Isolated eigenvalues of non Hermitian random matrices

**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**...

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### Eigenvalues of Euclidean Random Matrices

**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

**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

**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

**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

**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 ...

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### Eigenvalues and Spectral Dimension of Random Geometric Graphs in Thermodynamic Regime

**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**...

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### Large deviations for the largest eigenvalue of the sum of two random matrices

**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 ...

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