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arXiv · 2206.03444

Partially hyperbolic random dynamics on Grassmannians

Joris De Moor·Florian Dorsch·Hermann Schulz-Baldes
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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.

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Joris De Moor, Florian Dorsch, Hermann Schulz-Baldes. 2022-06-07. Partially hyperbolic random dynamics on Grassmannians. https://arxiv.org/abs/2206.03444

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