Dresden 2017 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
DY: Fachverband Dynamik und Statistische Physik
DY 13: Complex Systems
DY 13.2: Vortrag
Montag, 20. März 2017, 17:45–18:00, ZEU 147
Eigenvalue Outliers of Sparse non-Hermitian Random Matrices — •Izaak Neri1,2 and Fernando Metz3 — 1Max Planck Institute for the Physics of Complex Systems, Dresden, Germany — 2Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany — 3Universidade Federal de Santa Maria
Spectra of sparse non-Hermitian random matrices determine the dynamics of complex processes on graphs. Eigenvalue outliers in the spectrum are of particular interest, since they determine the stationary state and the stability of dynamical processes. We present a general and exact theory for the eigenvalue outliers of random matrices with a local tree structure. For adjacency and Laplacian matrices of oriented random graphs, we derive analytical expressions for the eigenvalue outliers, the first moments of the distribution of eigenvector elements associated with an outlier, the support of the spectral density, and the spectral gap. We show that these spectral observables obey universal expressions, which hold for a broad class of oriented random matrices.