Christian Mauduit: Measures of Pseudorandomness for Finite Binary Sequences

I will present a survey on recent results concerning pseudorandomness of finite binary sequences. In a series of papers, A. Sarkozy and myself introduced new measures of pseudorandomness connected to the regularity of the distribution relative to arithmetic progressions and the correlations. We analysed and compared several constructions including the Legendre symbol, the Thue-Morse sequence, the Rudin-Shapiro sequence, the Champernowne sequence, the Liouville function (jointly with J. Cassaigne, S. Ferenczi and J. Rivat), and a further construction due to P. Erdos related to a diophantine approximation problem. We also study the expectation and the minima of these measures and the connection between correlations of different order.

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