Pseudospectra and eigenvalue asymptotics for disordered non-selfadjoint operators in the semiclassical limit
M Vogel - Frontiers in Applied Mathematics and Statistics, 2024 - frontiersin.org
Pseudospectra and eigenvalue asymptotics for disordered non-selfadjoint operators in the
semiclassical limit Page 1 TYPE Mini Review PUBLISHED December DOI . /fams. . OPEN …
semiclassical limit Page 1 TYPE Mini Review PUBLISHED December DOI . /fams. . OPEN …
Gaussian regularization of the pseudospectrum and Davies' conjecture
A matrix is diagonalizable if it has a basis of linearly independent eigenvectors. Since the set
of nondiagonalizable matrices has measure zero, every is the limit of diagonalizable …
of nondiagonalizable matrices has measure zero, every is the limit of diagonalizable …
Outliers of random perturbations of Toeplitz matrices with finite symbols
A Basak, O Zeitouni - Probability Theory and Related Fields, 2020 - Springer
Abstract Consider an N * NN× N Toeplitz matrix T_N TN with symbol a (λ):= ∑ _ ℓ=-d_2^
d_1 a_ ℓ λ^ ℓ a (λ):=∑ ℓ=-d 2 d 1 a ℓ λ ℓ, perturbed by an additive noise matrix N^-γ E_N N-γ …
d_1 a_ ℓ λ^ ℓ a (λ):=∑ ℓ=-d 2 d 1 a ℓ λ ℓ, perturbed by an additive noise matrix N^-γ E_N N-γ …
Generalized Eigenspaces and Pseudospectra of Nonnormal and Defective Matrix-Valued Dynamical Systems
We consider nonnormal matrix-valued dynamical systems with discrete time. For an
eigenvalue of matrix, the number of times it appears as a root of the characteristic …
eigenvalue of matrix, the number of times it appears as a root of the characteristic …
Toeplitz band matrices with small random perturbations
J Sjöstrand, M Vogel - Indagationes Mathematicae, 2021 - Elsevier
We study the spectra of N× N Toeplitz band matrices perturbed by small complex Gaussian
random matrices, in the regime N≫ 1. We prove a probabilistic Weyl law, which provides a …
random matrices, in the regime N≫ 1. We prove a probabilistic Weyl law, which provides a …
General Toeplitz matrices subject to Gaussian perturbations
J Sjöstrand, M Vogel - Annales Henri Poincaré, 2021 - Springer
We study the spectra of general N * NN× N Toeplitz matrices given by symbols in the Wiener
Algebra perturbed by small complex Gaussian random matrices, in the regime N ≫ 1 N≫ 1 …
Algebra perturbed by small complex Gaussian random matrices, in the regime N ≫ 1 N≫ 1 …
Regularization of non-normal matrices by Gaussian noise—the banded Toeplitz and twisted Toeplitz cases
REGULARIZATION OF NON-NORMAL MATRICES BY GAUSSIAN NOISE—THE BANDED
TOEPLITZ AND TWISTED TOEPLITZ CASES Page 1 Forum of Mathematics, Sigma (2019) …
TOEPLITZ AND TWISTED TOEPLITZ CASES Page 1 Forum of Mathematics, Sigma (2019) …
Spectrum and pseudospectrum for quadratic polynomials in Ginibre matrices
NA Cook, A Guionnet, J Husson - … de l'Institut Henri Poincare (B) …, 2022 - projecteuclid.org
For a fixed quadratic polynomial p in n non-commuting variables, and n independent N× N
complex Ginibre matrices X 1 N,…, X n N, we establish the convergence of the empirical …
complex Ginibre matrices X 1 N,…, X n N, we establish the convergence of the empirical …
A probabilistic Weyl-law for perturbed Berezin–Toeplitz operators
I Oltman - Journal of Spectral Theory, 2023 - ems.press
A probabilistic Weyl-law for perturbed Berezin–Toeplitz operators Page 1 J. Spectr. Theory 13
(2023), 727–754 DOI 10.4171/JST/459 © 2023 European Mathematical Society Published by …
(2023), 727–754 DOI 10.4171/JST/459 © 2023 European Mathematical Society Published by …
Outliers of perturbations of banded Toeplitz matrices
C Bordenave, F Chapon, M Capitaine - arXiv preprint arXiv:2410.16439, 2024 - arxiv.org
Toeplitz matrices form a rich class of possibly non-normal matrices whose asymptotic
spectral analysis in high dimension is well-understood. The spectra of these matrices are …
spectral analysis in high dimension is well-understood. The spectra of these matrices are …