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

Christoph Aistleitner

doi:10.1112/blms/bdu052

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

Christoph Aistleitner

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the existence of a limit distribution for the normalized normality measureN(EN)/√N(asN→∞) for random binary sequences EN, by this means confirming a conjecture of Alon,Kohayakawa, Mauduit, Moreira and Rödl. The key point of the proof is to approximate thedistribution of the normality measure by the exiting probabilities of a multidimensional Wienerprocess from a certain polytope

Original language	English
Pages (from-to)	968-980
Journal	The Bulletin of the London Mathematical Society
Volume	46
Issue number	5
DOIs	https://doi.org/10.1112/blms/bdu052
Publication status	Published - 2014

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title = "On the limit distribution of the normality measure of random binary sequences",

abstract = "We prove the existence of a limit distribution for the normalized normality measureN(EN)/√N(asN→∞) for random binary sequences EN, by this means confirming a conjecture of Alon,Kohayakawa, Mauduit, Moreira and R{\"o}dl. The key point of the proof is to approximate thedistribution of the normality measure by the exiting probabilities of a multidimensional Wienerprocess from a certain polytope",

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AB - We prove the existence of a limit distribution for the normalized normality measureN(EN)/√N(asN→∞) for random binary sequences EN, by this means confirming a conjecture of Alon,Kohayakawa, Mauduit, Moreira and Rödl. The key point of the proof is to approximate thedistribution of the normality measure by the exiting probabilities of a multidimensional Wienerprocess from a certain polytope

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JO - The Bulletin of the London Mathematical Society

JF - The Bulletin of the London Mathematical Society

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

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