13 citations · 37 across the 13 of their papers we have counts for
16 papers
Pseudospectra and eigenvalue asymptotics for disordered non-selfadjoint operators in the semiclassical limit
Martin Vogel
The purpose of this note is to review some recent results concerning the pseudospectra and the eigenvalues asymptotics of non-selfadjoint semiclassical pseudo-differential operator…
Improved bounds for eigenfunctions under random perturbations in negative curvature
Maxime Ingremeau, Martin Vogel
It has been known since the work of Avakumovíc, Hörmander and Levitan that, on any compact smooth Riemannian manifold, if , then $\|ψ_λ\|_{L^\infty} \leq C λ^{\frac…
Emergence of Gaussian fields in noisy quantum chaotic dynamics
Maxime Ingremeau, Martin Vogel
We study the long time Schrödinger evolution of Lagrangian states on a compact Riemannian manifold of negative sectional curvature. We consider two models of semiclas…
Tunneling for the -operator
Johannes Sjöstrand, Martin Vogel
We study the small singular values of the -dimensional semiclassical differential operator on …
Localization of eigenvectors of non-Hermitian banded noisy Toeplitz matrices
Anirban Basak, Martin Vogel, Ofer Zeitouni
We prove localization with high probability on sets of size of order for the eigenvectors of non-Hermitian finitely banded Toeplitz matrices subject to…
Deterministic equivalence for noisy perturbations
Martin Vogel, Ofer Zeitouni
We prove a quantitative deterministic equivalence theorem for the logarithmic potentials of deterministic complex matrices subject to small random perturbations. We sho…
Almost sure Weyl law for quantized tori
Martin Vogel
We study the eigenvalues of the Toeplitz quantization of complex-valued functions on the torus subject to small random perturbations given by a complex-valued random matrix whose e…
General Toeplitz matrices subject to Gaussian perturbations
Johannes Sjoestrand, Martin Vogel
We study the spectra of general Toeplitz matrices given by symbols in the Wiener Algebra perturbed by small complex Gaussian random matrices, in the regime . We…
Toeplitz band matrices with small random perturbations
Johannes Sjoestrand, Martin Vogel
We study the spectra of Toeplitz band matrices perturbed by small complex Gaussian random matrices, in the regime . We prove a probabilistic Weyl law, which pro…
Semiclassical resolvent estimates for bounded potentials
Frédéric Klopp, Martin Vogel
We study the cut-off resolvent of semiclassical Schr{ö}dinger operators on with bounded compactly supported potentials . We prove that for real energies in…
Local eigenvalue statistics of one-dimensional random non-selfadjoint pseudo-differential operators
Stéphane Nonnenmacher, Martin Vogel
We consider a class of one-dimensional nonselfadjoint semiclassical pseudo-differential operators, subject to small random perturbations, and study the statistical properties of th…
Interior eigenvalue density of large bi-diagonal matrices subject to random perturbations
Johannes Sjoestrand, Martin Vogel
We study the spectrum of large a bi-diagonal Toeplitz matrix subject to a Gaussian random perturbation with a small coupling constant. We obtain a precise asymptotic description of…
Large bi-diagonal matrices and random perturbations
Johannes Sjoestrand, Martin Vogel
This is a first paper by the authors dedicated to the distribution of eigenvalues for random perturbations of large bidiagonal Toeplitz matrices.
Interior eigenvalue density of Jordan matrices with random perturbations
Johannes Sjoestrand, Martin Vogel
We study the eigenvalue distribution of a large Jordan block subject to a small random Gaussian perturbation. A result by E.B. Davies and M. Hager shows that as the dimension of th…
Two point eigenvalue correlation for a class of non-selfadjoint operators under random perturbations
Martin Vogel
We consider a non-selfadjoint -differential model operator in the semiclassical limit () subject to random perturbations with a small coupling constant …
The precise shape of the eigenvalue intensity for a class of non-selfadjoint operators under random perturbations
Martin Vogel
We consider a non-selfadjoint -differential model operator in the semiclassical limit () subject to small random perturbations. Furthermore, we let the cou…