7 citations · 8 across the 5 of their papers we have counts for
6 papers
Golden Ratio Nets and Sequences
Nathan Kirk, Christiane Lemieux, Jaspar Wiart
In this paper we introduce and study nets and sequences constructed in an irrational base, focusing on the case of a base given by the golden ratio . We provide a complete frame…
On the area of empty axis-parallel rectangles amidst 2-dimensional lattice points
Thomas Lachmann, Jaspar Wiart
The dispersion of a point set in the unit square is defined to be the area of the largest empty axis-parallel box. In this paper we are interested in the dispersion of lattices in…
On the distribution of scrambled -nets over unanchored boxes
C. Lemieux, J. Wiart
We introduce a new quality measure to assess randomized low-discrepancy point sets of finite size . This new quality measure, which we call "pairwise sampling dependence index",…
Improved dispersion bounds for modified Fibonacci lattices
Ralph Kritzinger, Jaspar Wiart
We study the dispersion of point sets in the unit square; i.e. the size of the largest axes-parallel box amidst such point sets. It is known that $\liminf_{N\to\infty} N\mathrm{dis…
Walsh functions, scrambled -nets, and negative covariance: applying symbolic computation to quasi-Monte Carlo integration
Jaspar Wiart, Elaine Wong
We investigate base Walsh functions for which the variance of the integral estimator based on a scrambled -net in base is less than or equal to that of the Monte-C…
On the dependence structure and quality of scrambled nets
Jaspar Wiart, Christiane Lemieux, Gracia Y. Dong
In this paper we develop a framework to study the dependence structure of scrambled -nets. It relies on values denoted by , which are related to how m…