138 citations · 788 across the 67 of their papers we have counts for
76 papers
The -Luxemburg Discrepancy for Nonnegative Weights Suffers from the Curse of Dimensionality
Josef Dick, Friedrich Pillichshammer
We study the normalized discrepancy in the Luxemburg norm generated by . For arbitrary nonnegative quadrature weights, we prove that the associated information com…
High Probability Derivative Bounds for Random tanh Neural Networks on a Hypercube
Josef Dick, Michael Feischl, Fabian Zehetgruber
We establish high-probability bounds for mixed input derivatives of wide random neural networks whose activation derivatives satisfy a factorial growth bound. Our main result speci…
Optimal Polynomial Tractability Exponents for the Inverse Star Discrepancy
Josef Dick
The inverse of the star discrepancy satisfies \[ d \varepsilon^{-1} \lesssim n^{\ast}(d,\varepsilon)\lesssim d\varepsilon^{-2} \] for all $d \in \mathbb{N}…
Second order interlaced polynomial lattice rules for integration over
Tiangang Cui, Josef Dick, Friedrich Pillichshammer
We study numerical integration of functions with respect to a probability measure. By applying the corresponding inverse cumulative distribution…
The star discrepancy of a union of randomly digitally shifted Korobov polynomial lattice point sets depends polynomially on the dimension
Josef Dick, Friedrich Pillichshammer
The star discrepancy is a quantitative measure of the uniformity of a point set in the unit cube. A central quantity of interest is the inverse of the star discrepancy, $N(\varepsi…
Lebesgue constants for the Walsh system and the discrepancy of the van der Corput sequence
Josef Dick, Friedrich Pillichshammer
In this short note we report on a coincidence of two mathematical quantities that, at first glance, have little to do with each other. On the one hand, there are the Lebesgue const…