Accumulation rate of bound states of dipoles generated by point charges in strained graphene - Dorsch, Florian (Journal of Mathematical Physics, 2017)
We consider strained graphene, modelled by the two-dimensional massive Diracoperator, with potentials corresponding to charge distributions with vanishing totalcharge, non-vanishing dipole moment and finitely many point charges of subcriti-cal coupling constants located in the graphene sheet. We show that the bound stateenergies accumulate exponentially fast at the edges of the spectral gap by deter-mining the leading order of the accumulation rat

Completeness of certain metric spaces of measures - Dorsch, Florian (Manuscripta Mathematica, 2022)
We prove that the set of finite Borel measures on a separable and directionally limited metric space (X, d) is complete with respect to the metric d(A)(mu, v) = sup (A is an element of A)vertical bar mu (A) - nu(A)vertical bar for all families of Borel sets A that contain every closed ball of X. This allows to prove the existence and uniqueness of the invariant Borel probability measure of certain Markov processes on X. A natural application is a Markov process induced by a random similitude.
CRIS-Team WoS Importer:2022-06-17

Partially hyperbolic random dynamics on Grassmannians - De Moor, Joris; Dorsch, Florian; Schulz-Baldes, Hermann (Journal of Mathematical Physics, 2023)
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.
CRIS-Team Scopus Importer:2023-09-01

Pseudo-gaps for random hopping models - Dorsch, Florian; Schulz-Baldes, Hermann (Journal of Physics A: Mathematical and Theoretical, 2020)
For one-dimensional random Schrodinger operators, the integrated density of states is known to be given in terms of the (averaged) rotation number of the Prufer phase dynamics. This paper develops a controlled perturbation theory for the rotation number around an energy at which all the transfer matrices commute and are hyperbolic. Such a hyperbolic critical energy appears in random hopping models. The main result is a Holder continuity of the rotation number at the critical energy that implies the existence of a pseudo-gap. The proof uses renewal theory. The result is illustrated by numerics.
CRIS-Team WoS Importer:2020-05-05

RANDOM MOBIUS DYNAMICS ON THE UNIT DISC AND PERTURBATION THEORY FOR LYAPUNOV EXPONENTS - Dorsch, Florian; Schulz-Baldes, Hermann (Discrete and Continuous Dynamical Systems-Series B, 2022)
Randomly drawn 2 x 2 matrices induce a random dynamics on the Riemann sphere via the Mobius transformation. Considering a situation where this dynamics is restricted to the unit disc and given by a random rotation perturbed by further random terms depending on two competing small parameters, the invariant (Furstenberg) measure of the random dynamical system is determined. The results have applications to the perturbation theory of Lyapunov exponents which are of relevance for one-dimensional discrete random Schrodinger operators.
CRIS-Team WoS Importer:2021-11-26

Random perturbations of hyperbolic dynamics - Dorsch, Florian; Schulz-Baldes, Hermann (Electronic Journal of Probability, 2019)
A sequence of large invertible matrices given by a small random perturbation around a fixed diagonal and positive matrix induces a random dynamics on a high-dimensional sphere. For a certain class of rotationally invariant random perturbations it is shown that the dynamics approaches the stable fixed points of the unperturbed matrix up to errors even if the strength of the perturbation is large compared to the relative increase of nearby diagonal entries of the unperturbed matrix specifying the local hyperbolicit