Torben Krüger

Coexistence and survival in conservative Lotka-Volterra networks.

Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks in which the total biomass is conserved is of vital importance for the characterization of long-term dynamics of ecological communities. Here, we introduce a classification scheme for coexistence scenarios in these conservative LV models and quantify the extinction process by employing the Pfaffian of the networks interaction matrix. We illustrate our findings on global stability properties for general systems of four and five species and find a generalized scaling law for the extinction time.

Universality for general Wigner-type matrices

We consider the local eigenvalue distribution of large self-adjoint

Local Spectral Statistics of Gaussian Matrices with Correlated Entries

N\times N

Local law for random Gram matrices

N×N random matrices

Stability of the matrix Dyson equation and random matrices with correlations

\mathbf {H}=\mathbf {H}^*

Local eigenvalue statistics for random matrices with general short range correlations

H=H∗ with centered independent entries. In contrast to previous works the matrix of variances