The problem of finding the largest empty axis-parallel box amidst a point configuration is a classical problem in computational complexity theory. It is known that the volume of the largest empty boxâ€¦ (More)

We show new lower bounds for the star-discrepancy and its inverse for subsets of the unit cube. They are polynomial in the quotient d/n of the number n of sample points and the dimension d. Theyâ€¦ (More)

We prove the curse of dimensionality for multivariate integration of Ck functions. The proofs are based on volume estimates for k = 1 together with smoothing by convolution. This allows us to obtainâ€¦ (More)

The L2-discrepancy measures the irregularity of the distribution of a finite point set. In this note, we prove lower bounds for the L2-discrepancy of arbitrary N-point sets. Our main focus is on theâ€¦ (More)

We prove a variant of a Johnson-Lindenstrauss lemma for matrices with circulant structure. This approach allows to minimise the randomness used, is easy to implement and provides good running times.â€¦ (More)

We consider the problem of integration of d-variate analytic functions defined on the unit cube with directional derivatives of all orders bounded by 1. We prove that the Clenshaw Curtis Smolyakâ€¦ (More)

We investigate quasi-Monte Carlo rules for the numerical integration of multivariate periodic functions from Besov spaces Sp,q B(T d)with dominating mixed smoothness 1/p < r < 2. We show that order 2â€¦ (More)