On lower bounds for the L2-discrepancy

@article{Hinrichs2011OnLB,
  title={On lower bounds for the L2-discrepancy},
  author={Aicke Hinrichs and Lev Markhasin},
  journal={J. Complexity},
  year={2011},
  volume={27},
  pages={127-132}
}
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 the two-dimensional case. Asymptotic upper and lower estimates of the L2-discrepancy in dimension 2 are well known, and are of the sharp order √ logN . Nevertheless, the gap in the constants between the best-known lower and upper bounds is unsatisfactorily large for a two-dimensional problem. Our lower… CONTINUE READING