de Moor J, Dorsch F, Schulz-Baldes H (2023)
Publication Type: Journal article
Publication year: 2023
Book Volume: 64
Article Number: 082702
Journal Issue: 8
DOI: 10.1063/5.0146402
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.
APA:
de Moor, J., Dorsch, F., & Schulz-Baldes, H. (2023). Partially hyperbolic random dynamics on Grassmannians. Journal of Mathematical Physics, 64(8). https://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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