Estimates of the Discrepancy Function in Exponential Orlicz Spaces

Analysis Seminar
Wednesday, March 13, 2013 - 14:00
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech
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.