6 citations · 9 across the 13 of their papers we have counts for
19 papers
Dimensions of Orbit Closures and Discrepancy for Dynamical -adic Sequences
Keivan Mallahi Karai, Christian Weiß
Classical discrepancy quantifies the irregularity of the distribution of a sequence in the unit interval. In this paper, we study the analogous notion for sequences in the ring of…
A p-adic Poissonian Pair Correlation Concept
Christian Weiss
The pair correlation statistic is an important concept in real uniform distribution theory. Therefore, sequences in the unit interval with (weak) Poissonian pair correlations have…
On the finite pair correlation function of van der Corput sequences
Christian Weiß
In this note we derive an explicit formula for the finite empiric pair correlation function of the van der Corput sequence in base for all and $s \g…
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…
A study in quantitative equidistribution on the unit square
Max Goering, Christian Weiss
The distributional properties of the translation flow on the unit square have been considered in different fields of mathematics, including algebraic geometry and discrepancy theor…
Some Connections Between Discrepancy, Finite Gap Properties, and Pair Correlations
Christian Weiß
A generic uniformly distributed sequence in possesses Poissonian pair correlations (PPC). Vice versa, it has been proven that a sequence with PPC…
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…
A Generalized Faulhaber Inequality, Improved Bracketing Covers, and Applications to Discrepancy
Michael Gnewuch, Hendrik Pasing, Christian Weiß
We prove a generalized Faulhaber inequality to bound the sums of the -th powers of the first (possibly shifted) natural numbers. With the help of this inequality we are able…
Discrepancy Properties and Conjugacy Classes of Interval Exchange Transformations
Christian Weiß
Interval exchange transformations are typically uniquely ergodic maps and therefore have uniformly distributed orbits. Their degree of uniformity can be measured in terms of the st…
Families of well approximable measures
Samantha Fairchild, Max Goering, Christian Weiß
We provide an algorithm to approximate a finitely supported discrete measure by a measure corresponding to a set of points so that the total variation between a…
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…
Deducing Three Gap Theorem From Rauzy-Veech Induction
Christian Weiß
The Three Gap Theorem states that there are at most three distinct lengths of gaps if one places points on a circle, at angles of from the starting point…
Interval Exchange Transformations and Low-Discrepancy
Christian Weiß
In [Mas82] and [Vee78] it was proved independently that almost every interval exchange transformation is uniquely ergodic. The Birkhoff ergodic theorem implies that these maps main…
On the Classification of LS-Sequences
Christian Weiß
This paper adresses the question whether the -sequences constructed by Carbone yield indeed a new family of low discrepancy sequences. While it is well known that the case $S=0…
Non-congruence of homology Veech groups in genus two
Christian Weiß
We study the action of the Veech group of square-tiled surfaces of genus two on homology. This action defines the homology Veech group which is a subgroup of $\textrm{SL}_2(\mathca…
Twisted Teichmüller curves
Christian Weiß
Let denote the Hilbert modular surface $\HH \times \HH^- / \SL_2(\OD)$. In \cite{HZ76}, F. Hirzebruch and D. Zagier introduced Hirzebruch-Zagier cycles, that could also be ca…