4 papers
On the Pair Correlation Statistic of Sequences with Finite Gap Property
Jasmin Fiedler, Christian Weiß
The limiting function of the pair correlation \[ \frac{1}{N} \# \left\{ 1 \leq i\neq j\leq N \middle\vert \left\lVert x_i - x_j \right\rVert \leq \frac{s}{N} \right\} \] for…
Poissonian pair correlations for dependent random variables
Jasmin Fielder, Michael Gnewuch, Christian Weiß
We consider Poissonian pair correlations (PPC) for uniformly distributed sequences of random numbers with a dependency structure. More specifically, we treat two classes of depende…
Weak Poissonian box correlations of higher order
Jasmin Fiedler, Christian Weiß
Poissonian pair correlations have sparked interest within the mathematical community, because of their number theoretic properties, and their connections to quantum physics and pro…
New Bounds for the Extreme and the Star Discrepancy of Double-Infinite Matrices
Jasmin Fiedler, Michael Gnewuch, Christian Weiß
According to Aistleitner and Weimar, there exist two-dimensional (double) infinite matrices whose star-discrepancy of the first rows and columns, interpreted as…