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Dresden 2017 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 13: Complex Systems

DY 13.2: Talk

Monday, March 20, 2017, 17:45–18:00, ZEU 147

Eigenvalue Outliers of Sparse non-Hermitian Random Matrices — •Izaak Neri1,2 and Fernando Metz31Max 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.

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