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UID:8102@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20150414T110000
DTEND;TZID=Europe/Paris:20150414T114000
DTSTAMP:20241120T210029Z
URL:https://www.i2m.univ-amu.fr/evenements/normality-computability-and-ran
 domness/
SUMMARY:Robert F. Tichy (Technische Universität Graz): Normality\, Computa
 bility and Randomness
DESCRIPTION:Robert F. Tichy: In the first part we start from the concept of
  normal numbers with respect to a given base and present some recent metho
 ds of explicit constructions. Furthermore\, we present a dynamical interpr
 etation and extensions to absolutely normal numbers. This concept is inves
 tigated from a computational point of view\, extending some results of A. 
 Turing. The second part of the lecture is devoted to van der Corput sets a
 nd sets of recurrence. We give new constructions involving equidistributio
 n of sequences of prime powers. This refines and unifies earlier results o
 btained by Sárközy\, Furstenberg\, Kamae and Mendés-France and Bergelso
 n and Lesigne. The proofs heavily depend on analytic machinery involving b
 ounds for exponential sums. In the third part of the lecture we give some 
 new sharp result concerning the probabilistic behaviour of lacunary sequen
 ces. In particular we show limit theorems for discrepancy functions and re
 lated quantities. This leads to quantitative results in the theory of norm
 al numbers and pseudorandomness.\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Robert_F_Tichy.jpg
CATEGORIES:Séminaire,Ernest
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DTSTART:20150329T030000
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