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- W1606417300 abstract "We prove a law of the iterated logarithm for the Kolmogorov-Smirnov statistic, or equivalently, the discrepancy of sequences $(n_{k}omega)$ mod $1$. Here $(n_{k})$ is a sequence of integers satisfying a sub-Hadamard growth condition and such that linear Diophantine equations in the variables $n_{k}$ do not have too many solutions. The proof depends on a martingale embedding of the empirical process; the number-theoretic structure of $(n_k)$ enters through the behavior of the square function of the martingale." @default.
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- W1606417300 date "2006-01-01" @default.
- W1606417300 modified "2023-09-25" @default.
- W1606417300 title "Empirical processes in probabilistic number theory: the LIL for the discrepancy of $(nsb komega)bmod1$" @default.
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- W1606417300 doi "https://doi.org/10.1215/ijm/1258059472" @default.
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