@article{10902/35966,
year = {2019},
month = {6},
url = {https://hdl.handle.net/10902/35966},
abstract = {In this note we study the pair correlation statistics for the sequence of shifts of α, xn = {2n α}, n = 1, 2, 3, . . ., where we choose α as the Champernowne constant in base 2. Throughout this article {·} denotes the fractional part of a real number. It is well known that (xn)n∈N has Poissonian pair correlations for almost all normal numbers α (in the sense of Lebesgue), but we will show that it does not have this property for all normal numbers α, as it fails to be Poissonian for the Champernowne constant.},
organization = {The first author is supported by the Austrian Science Fund (FWF), Project P27351-N26. The second author is supported by the Austrian Science Fund (FWF), Project F5507-N26, which is a part of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications”.},
publisher = {Adam Mickiewicz University},
publisher = {Functiones et Approximatio, Commentarii Mathematici, 2019, 60(2), 253-262},
title = {The champernowne constant is not poissonian},
author = {Pirsic, Ísabel and Stockinger, Wolfgang},
}