Séminaire du LPTMS: Gernot Akemann


11:00 - 12:00

LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay
15 Rue Georges Clemenceau, Orsay, 91405

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Universal Lyapunov Exponents from Products of Random Matrices

Gernot Akemann, Universität Bielefeld

Random Matrices find many applications in Physics and Mathematics. In particular products of random matrices can be used as a simple model for linear time evolution. In this talk I will review recent progress on an exact solution of this model for Gaussian random matrices. Both the spectral statistic of its complex eigenvalues and its real positive singular values are given by a determinantal point process with an underlying integrable kernel. In the limit of an infinite product the Lyapunov exponents become deterministic and we compute their variances and higher order cumulants. Remarkably the moduli of the complex eigenvalues and the singular values become identical in this limit. We will also discuss universality and possible extensions.

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