Estimates of the Discrepancy Function in Exponential Orlicz Spaces

Analysis Seminar
Wednesday, March 13, 2013 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Gagik Amirkhanyan – Georgia Tech
Brett Wick
For dimensions n greater than or equal to 3, and integers N greater than 1, there is a distribution of points P in a unit cube [0,1]^{n}, of cardinality N, for which the discrepancy function D_N associated with P has an optimal Exponential Orlicz norm. In particular the same distribution will have optimal L^p norms, for 1 < p < \infty. The collection P is a random digit shift of the examples of W.L. Chen and M. Skriganov.