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On the limit distribution of the well-distribution measure of random binary sequences. (English. French summary) Zbl 1282.11094

Summary: We prove the existence of a limit distribution of the normalized well-distribution measure \(W(E_{N})/N\) (as \(N\rightarrow \infty\)) for random binary sequences \(E_{N}\), by this means solving a problem posed by N. Alon et al. [Proc. Lond. Math. Soc. (3) 95, No. 3, 778–812 (2007; Zbl 1124.68084)].

MSC:

11K38 Irregularities of distribution, discrepancy
60F10 Large deviations
60G50 Sums of independent random variables; random walks
11K45 Pseudo-random numbers; Monte Carlo methods

Citations:

Zbl 1124.68084
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References:

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[2] N. Alon, Y. Kohayakawa, C. Mauduit, C. G. Moreira, and V. Rödl. Measures of pseudorandomness for finite sequences: typical values. Proc. Lond. Math. Soc. (3), 95(3) (2007), 778-812. · Zbl 1124.68084
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