ON-LINE QLunch: Torben Krüger

Spectral statistics of random matrices often exhibit universal behaviour as the dimension grows to infinity. On the global scale of the entire spectrum the empirical eigenvalue distribution con- centrates around a deterministic limit; while on the smallest local scale of the eigenvalue spacing, the k-point correlation functions become universal, depending only on the symmetry class of the matrix but not on any model details. For selfadjoint models this fact has been established in great generality. However, for non-selfadjoint models with eigenvalues in the complex plane their inher- ent spectral instability poses a major challenge for the study of local eigenvalue statistics. We will present recent results on controlling eigenvalue spectra for non-selfadjoint random matrices down to all scales above the eigenvalue spacing and their application to systems of randomly coupled differential equations that are used to model a wide range of disordered dynamical systems ranging from neural networks to food webs.
[Joint work with the Johannes Alt, László Erdős and David Renfrew]

Suzanne Andersen is inviting you to a scheduled Zoom meeting.

Topic: QLunch on April 22: Torben Krüger

Time: Apr 22, 2020 12:00 PM Copenhagen

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https://ucph-ku.zoom.us/j/61730175237

Meeting ID: 617 3017 5237