Poisson generic real numbers
Verónica Becher (Universidad de Buenos Aires & CONICET Argentina)
Abstract: Years ago Zeev Rudnick defined the Poisson generic real numbers as those where the number of occurrences of the long strings in the initial segments of their fractional expansions in some base have the Poisson distribution. Yuval Peres and Benjamin Weiss proved that almost all real numbers, with respect to Lebesgue measure, are Poisson generic. They also showed that Poisson genericity implies Borel normality but the two notions do not coincide, witnessed by the famous Champernowne constant. We recently showed that there are computable Poisson generic real numbers and that all Martin-Löf real numbers are Poisson generic. This is joint work Nicolás Álvarez and Martín Mereb.
dynamical systemsnumber theory
Audience: researchers in the topic
( paper )
Series comments: Description: Online seminar on numeration systems and related topics
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Organizers: | Shigeki Akiyama, Ayreena Bakhtawar, Karma Dajani, Kevin Hare, Hajime Kaneko, Niels Langeveld, Lingmin Liao, Wolfgang Steiner* |
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