8 papers
Approximation of Discrete Measures by Finite Point Sets
Christian Weiß
For a probability measure on without discrete component, the best possible order of approximation by a finite point set in terms of the star-discrepancy is $\frac{1}{2N…
Remarks on the Pair Correlation Statistic of Kronecker Sequences and Lattice Point Counting
Christian Weiß
In this short note, we reformulate the task of calculating the pair correlation statistics of a Kronecker sequence as a lattice point counting problem. This can be done analogously…
Systems of Rank One, Explicit Rokhlin Towers, and Covering Numbers
Christian Weiß
Rotations of the one-dimensional torus (equipped with the normalized Lebesgue measure) by an irrational angle are known to be dynamical systems of rank one. This is equiv…
Multi-dimensional Kronecker Sequences with a Small Number of Gap Lengths
Christian Weiß
Recently, generalizations of the classical Three Gap Theorem to higher dimensions attracted a lot of attention. In particular, upper bounds for the number of nearest neighbor dista…
Sequences with almost Poissonian Pair Correlations
Christian Weiß, Thomas Skill
Although a generic uniformly distributed sequence has Poissonian pair correlations, only one explicit example has been found up to now. Additionally, it is even known that many cla…
Improving a Constant in High-Dimensional Discrepancy Estimates
Hendrik Pasing, Christian Weiß
For all and there exist sequences in such that the star-discrepancy of these points can be bounded by $$D_N^*(z_1,\ldots,z_N) \le…