This talk is devoted to the relation between empirical process theory and problems concerning the existence of low-discrepancy point sets and the tractability of multivariate integration. First we recall some definitions and basic results concerning empirical processes indexed by sets. Then we show how the distributional behaviour of these processes depends on the entropy of the underlying class of test sets. Finally we show how large deviation bounds for empirical processes can be used to obtain existence results for high-dimensional low-discrepancy point sets and corresponding tractability results for multivariate integration. We report on recent progress and discuss some open problems.
Christoph Aistleitner is currently a Schrödinger fellow of the Austrian Science Fund FWF. He has been working as a guest researcher in the Department of Applied Mathematics of UNSW for one year, and is now about to leave.