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arXiv · 1301.6454

On the limit distribution of the normality measure of random binary sequences

Christoph Aistleitner
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Abstract

We prove the existence of a limit distribution for the normalized normality measure $\mathcal{N}(E_N)/\sqrt{N}$ (as $N \to \infty$) for random binary sequences $E_N$, by this means confirming a conjecture of Alon, Kohayakawa, Mauduit, Moreira and R{ö}dl. The key point of the proof is to approximate the distribution of the normality measure by the exiting probabilities of a multidimensional Wiener process from a certain polytope.

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Christoph Aistleitner. 2014-04-03. On the limit distribution of the normality measure of random binary sequences. https://doi.org/10.1112/blms%2Fbdu052

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