Aicke Hinrichs

Covering numbers, vapnik-červonenkis classes and bounds for the star-discrepancy

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. They provide the best-known lower bounds for n not too large compared with d.

Johnson-Lindenstrauss lemma for circulant matrices

We prove a variant of a Johnson-Lindenstrauss lemma for matrices with circulant structure. This approach allows to minimize the randomness used, is easy to implement and provides good running times. The price to be paid is the higher dimension of the target space k = O(e−2 log3 n) instead of the classical bound k = O(e−2 log n).

New sets with large Borsuk numbers

Abstract We construct finite sets in R n , n⩾298, which cannot be partitioned into n+11 parts of smaller diameter thus decreasing the smallest dimension in which Borsuks conjecture is known to be false.

Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions

We investigate quasi-Monte Carlo rules for the numerical integration of multivariate periodic functions from Besov spaces

Tractability properties of the weighted star discrepancy

S^r_{p,q}B(\mathbb {T}^d)

On lower bounds for the L2-discrepancy

Sp,qrB(Td) with dominating mixed smoothness

Equivalence of anchored and ANOVA spaces via interpolation

1/p<r<2