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# 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} }

- Published 2011 in J. Complexity
DOI:10.1016/j.jco.2010.11.002

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