Robert Tichy, Pseudorandomness: an analysis via number-theoretic methods

Pseudorandomness: an analysis via number-theoretic methods

Robert Tichy, TU Graz

Donald Knuth formulated in his classical book "The Art of Computer Programming" various number-theoretic criteria to describe (pseudo)randomness of sequences of reals or integers. This includes normality and correlation measures. Quantitative versions of these concepts can be established in terms of the so-called discrepancy function. In the present talk the focus lies on limit laws for lacunary sequences and on new estimates of the well-distribution and correlation measure in the sense of Mauduit and Sarkoezy for binary sequences. Finally, we give some applications to diophantine approximation, difference sets and arithmetic dynamical systems.

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