AG Mathematische Physik, Joris De Moor (FAU): Partially hyperbolic random dynamics on Grassmannians

Joris De Moor

Partially hyperbolic random dynamics on Grassmannians

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 on average 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.