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Mathematics > Number Theory

arXiv:2202.01632 (math)
[Submitted on 3 Feb 2022 (v1), last revised 12 Aug 2022 (this version, v3)]

Title:Poisson generic sequences

Authors:Nicolás Álvarez, Verónica Becher, Martín Mereb
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Abstract:Years ago, Zeev Rudnick defined the Poisson generic real numbers by counting the number of occurrences of long blocks of digits in the initial segments of the expansions of the real numbers in a fixed integer base. Peres and Weiss proved that almost all real numbers, with respect to Lebesgue measure, are Poisson generic, but they did not publish their proof. In this note first we transcribe Peres and Weiss' proof and then we show that there are computable Poisson generic instances and that all Martin-Löf random real numbers are Poisson generic.
Subjects: Number Theory (math.NT)
MSC classes: 11K16, 11K55, 60G55
Cite as: arXiv:2202.01632 [math.NT]
  (or arXiv:2202.01632v3 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.2202.01632

Submission history

From: Verónica Becher [view email]
[v1] Thu, 3 Feb 2022 15:03:45 UTC (12 KB)
[v2] Sat, 28 May 2022 04:48:24 UTC (15 KB)
[v3] Fri, 12 Aug 2022 21:29:16 UTC (16 KB)
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