1 citations · 1 across the 1 of their papers we have counts for
5 papers
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…
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…
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, $…
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…