A sharp lower bound for discrepancy on R / Z is derived that resembles the upper bound due to LeVeque. An analogous bound is proved for discrepancy on Rk / Zk. These are discussed in the more general context of the discrepancy of probablity measures. As applications, the bounds are applied to Kronecker sequences and to a random walk on the torus.
© 2000 Springer-Verlag
Francis Edward Su. A LeVeque-type lower bound for discrepancy. In Monte Carlo and quasi-Monte Carlo methods 1998 (Claremont, CA), pages 448–458. Springer, Berlin, 2000.