36 citations · 115 across the 12 of their papers we have counts for
18 papers
Critical Erd{\H o}s-Rényi digraph: all eigenvectors away from zero are delocalized
Johannes Alt, Sarah Timhadjelt
We consider the adjacency matrix of the directed Erd{\H o}s-Rényi graph. As long as the expected degree is larger than the logarithm of the number of vertices, the graph is connect…
Brown measures of deformed -valued circular elements
Johannes Alt, Torben Krüger
We consider the Brown measure of , where lies in a commutative tracial von Neumann algebra and is a -valued circular e…
Spectrum occupies pseudospectrum for random matrices with diagonal deformation and variance profile
Johannes Alt, Torben Krüger
We consider non-Hermitian random matrices with independent entries and a variance profile, as well as an additive deterministic diagonal deformation. We show that their…
Localized phase for the Erdős-Rényi graph
Johannes Alt, Raphael Ducatez, Antti Knowles
We analyse the eigenvectors of the adjacency matrix of the Erdős-Rényi graph for . We show the existence of a localized phas…
The completely delocalized region of the Erdős-Rényi graph
Johannes Alt, Raphael Ducatez, Antti Knowles
We analyse the eigenvectors of the adjacency matrix of the Erdős-Rényi graph on vertices with edge probability . We determine the full region of delocalization by…
Poisson statistics and localization at the spectral edge of sparse Erdős-Rényi graphs
Johannes Alt, Raphael Ducatez, Antti Knowles
We consider the adjacency matrix of the Erdős-Rényi graph on vertices with edge probability . For , we prove that the eigenvalue…
Local elliptic law
Johannes Alt, Torben Krüger
The empirical eigenvalue distribution of the elliptic random matrix ensemble tends to the uniform measure on an ellipse in the complex plane as its dimension tends to infinity. We…
Delocalization transition for critical Erdős-Rényi graphs
Johannes Alt, Raphael Ducatez, Antti Knowles
We analyse the eigenvectors of the adjacency matrix of a critical Erdős-Rényi graph , where is of order . We show that its spectrum splits into two ph…
Inhomogeneous Circular Law for Correlated Matrices
Johannes Alt, Torben Krüger
We consider non-Hermitian random matrices with general decaying correlations between their entries. For large , the empirical spectral distributi…
Spectral radius of random matrices with independent entries
Johannes Alt, Laszlo Erdos, Torben Krüger
We consider random matrices with independent and centered entries and a general variance profile. We show that the spectral radius of converges with very high p…
Extremal eigenvalues of critical Erdős-Rényi graphs
Johannes Alt, Raphaël Ducatez, Antti Knowles
We complete the analysis of the extremal eigenvalues of the the adjacency matrix of the Erdős-Rényi graph in the critical regime of the transition…
The Dyson equation with linear self-energy: spectral bands, edges and cusps
Johannes Alt, Laszlo Erdos, Torben Krüger
We study the unique solution of the Dyson equation \[ -m(z)^{-1} = z - a + S[m(z)] \] on a von Neumann algebra with the constraint . Here, $…
Correlated Random Matrices: Band Rigidity and Edge Universality
Johannes Alt, László Erdős, Torben Krüger +1
We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal ed…
Singularities of the density of states of random Gram matrices
Johannes Alt
For large random matrices with independent, centered entries but not necessarily identical variances, the eigenvalue density of is well-approximated by a deterministic m…
Location of the spectrum of Kronecker random matrices
Johannes Alt, Laszlo Erdos, Torben Krüger +1
For a general class of large non-Hermitian random block matrices we prove that there are no eigenvalues away from a deterministic set with very high probability. This…
Local inhomogeneous circular law
Johannes Alt, Laszlo Erdos, Torben Krüger
We consider large random matrices with centered, independent entries which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectr…
Local law for random Gram matrices
Johannes Alt, László Erdős, Torben Krüger
We prove a local law in the bulk of the spectrum for random Gram matrices , a generalization of sample covariance matrices, where is a large matrix with independent, cent…
The Local Semicircle Law for Random Matrices with a Fourfold Symmetry
Johannes Alt
We consider real symmetric and complex Hermitian random matrices with the additional symmetry . The matrix elements are independent (up to the fourfold symmetry…