A LeVeque-type lower bound for discrepancy
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 R k/Z k. These are discussed in the more general context of the discrepancy of probability measures. As applications, the bounds are applied to Kronecker sequences and to a random walk on the torus.
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