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Conference Papers Year : 2012

Pseudo-randomness of a random Kronecker sequence

Abstract

We study two randomness measures for the celebrated Kroneckersequence S(!) formed by the fractional parts of the multiples ofa real !. The first measure is the well-known discrepancy, whereas theother one, the Arnold measure, is less popular. Both describe the behaviourof the truncated sequence ST (!) formed with the first T terms,for T !". We perform a probabilistic study of the pseudorandomnessof the sequence S(!) (discrepancy and Arnold measure), and we giveestimates of their mean values in two probabilistic settings : the input !may be either a random real or a random rational. The results exhibitstrong similarities between the real and rational cases; they also showthe influence of the number T of truncated terms, via its relation to thecontinued fraction expansion of !.
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Dates and versions

hal-01084963 , version 1 (20-11-2014)

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Eda Cesaratto, Brigitte Vallée. Pseudo-randomness of a random Kronecker sequence. Latin American Symposium on Theoretical Informatics, Apr 2012, Arequipa, Peru. pp.157-171, ⟨10.1007/978-3-642-29344-3_14⟩. ⟨hal-01084963⟩
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