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math.PR2026
On the Integrated Density of States of Fractional Random Schrödinger Operators
Peter Kern, Leonard Pleschberger
We proof the existence of the Integrated Density of States (IDS) for fractional random Schrödinger operators with Gaussian potential based on the theory of isotropic -stable Lév…
math.PR2026
Discrete Hyperbolic Secant Distributions
Leonard Pleschberger
We introduce a family of discrete hyperbolic secant distributions on , whose normalizing constants arise from series values calculated by Ramanujan and are expressed in…
math.PR2023
Parabolic Fractal Geometry of Stable Lévy Processes with Drift
Peter Kern, Leonard Pleschberger
We explicitly calculate the Hausdorff dimension of the graph and range of an isotropic stable Lévy process plus deterministic drift function . For that purpose we use a rest…