Add to ORKGWe show that there is a constant $K > 0$ such that for all $N, s \in \N$, $s \le N$, the point set consisting of $N$ points chosen uniformly at random in the $s$-dimensional unit cube $[0,1]^s$ with probability at least $1-\exp(-\Theta(s))$ admits an axis parallel rectangle $[0,x] \subseteq [0,1]^s$ containing $K \sqrt{sN}$ points more than expected. Consequently, the expected star discrepancy of a random point set is of order $\sqrt{s/N}$
A lower bound for the length of the shortest path through n points in [0, Ild is given in terms of t...
AbstractWe study the problem of discrepancy of finite point sets in the unit square with respect to ...
AbstractIn many applications it has been observed that hybrid-Monte Carlo sequences perform better t...
We show that there is a constant $K > 0$ such that for all $N, s \in \N$, $s \le N$, the point set c...
A mixed sequence is a sequence in the $s$-dimensional unit cube which one obtains by concatenating a...
We present a new algorithm for estimating the star discrepancy of arbitrary point sets. Similar to t...
For $m, d \in {\mathbb N}$, a jittered sampling point set $P$ having $N = m^d$ points in $[0,1)^d$ i...
AbstractFor numerical integration in higher dimensions, bounds for the star-discrepancy with polynom...
AbstractWe provide a deterministic algorithm that constructs small point sets exhibiting a low star ...
AbstractThe well-known star discrepancy is a common measure for the uniformity of point distribution...
A sharp lower bound for discrepancy on R / Z is derived that resembles the upper bound due to LeVequ...
AbstractThe L2-discrepancy measures the irregularity of the distribution of a finite point set. In t...
We study the discrepancy of jittered sampling sets: such a set P⊂ [0,1]d is generated for fixed m∈ℕ ...
AbstractWe propose an algorithm to compute upper and lower bounds for the star discrepancy of an arb...
AbstractWe show new lower bounds for the star-discrepancy and its inverse for subsets of the unit cu...
A lower bound for the length of the shortest path through n points in [0, Ild is given in terms of t...
AbstractWe study the problem of discrepancy of finite point sets in the unit square with respect to ...
AbstractIn many applications it has been observed that hybrid-Monte Carlo sequences perform better t...
We show that there is a constant $K > 0$ such that for all $N, s \in \N$, $s \le N$, the point set c...
A mixed sequence is a sequence in the $s$-dimensional unit cube which one obtains by concatenating a...
We present a new algorithm for estimating the star discrepancy of arbitrary point sets. Similar to t...
For $m, d \in {\mathbb N}$, a jittered sampling point set $P$ having $N = m^d$ points in $[0,1)^d$ i...
AbstractFor numerical integration in higher dimensions, bounds for the star-discrepancy with polynom...
AbstractWe provide a deterministic algorithm that constructs small point sets exhibiting a low star ...
AbstractThe well-known star discrepancy is a common measure for the uniformity of point distribution...
A sharp lower bound for discrepancy on R / Z is derived that resembles the upper bound due to LeVequ...
AbstractThe L2-discrepancy measures the irregularity of the distribution of a finite point set. In t...
We study the discrepancy of jittered sampling sets: such a set P⊂ [0,1]d is generated for fixed m∈ℕ ...
AbstractWe propose an algorithm to compute upper and lower bounds for the star discrepancy of an arb...
AbstractWe show new lower bounds for the star-discrepancy and its inverse for subsets of the unit cu...
A lower bound for the length of the shortest path through n points in [0, Ild is given in terms of t...
AbstractWe study the problem of discrepancy of finite point sets in the unit square with respect to ...
AbstractIn many applications it has been observed that hybrid-Monte Carlo sequences perform better t...