Partially hyperbolic random dynamics on Grassmannians

de Moor J, Dorsch F, Schulz-Baldes H (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Journal of Mathematical Physics American Institute of Physics (AIP)

Book Volume: 64

Article Number: 082702

Journal Issue: 8

DOI: 10.1063/5.0146402

Abstract

A sequence of invertible matrices given by a small random perturbation around a fixed diagonal partially hyperbolic matrix induces a random dynamics on the Grassmann manifolds. Under suitable weak conditions, it is known to have a unique invariant (Furstenberg) measure. The main result gives concentration bounds on this measure, showing that with high probability, the random dynamics stays in the vicinity of stable fixed points of the unperturbed matrix, in a regime where the strength of the random perturbation dominates the local hyperbolicity of the diagonal matrix. As an application, bounds on sums of Lyapunov exponents are obtained.

Authors with CRIS profile

Joris de Moor Professur für Mathematik (Mathematische Physik) Florian Dorsch Professur für Mathematik (Mathematische Physik) Hermann Schulz-Baldes Professur für Mathematik (Mathematische Physik)

How to cite

APA:

de Moor, J., Dorsch, F., & Schulz-Baldes, H. (2023). Partially hyperbolic random dynamics on Grassmannians. Journal of Mathematical Physics, 64(8). https://dx.doi.org/10.1063/5.0146402

MLA:

de Moor, Joris, Florian Dorsch, and Hermann Schulz-Baldes. "Partially hyperbolic random dynamics on Grassmannians." Journal of Mathematical Physics 64.8 (2023).

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