Niederreiter and Halton sequences fail to satisfy Poissonian pair correlations in any dimension, confirming Larcher and Stockinger's conjecture.
On Pair Correlation of Sequences
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We give a survey on the concept of Poissonian pair correlation (PPC) of sequences in the unit interval, on existing and recent results and we state a list of open problems. Moreover, we present and discuss a quite recent multi-dimensional version of PPC.
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Pair Correlations of Niederreiter and Halton Sequences are not Poissonian
Niederreiter and Halton sequences fail to satisfy Poissonian pair correlations in any dimension, confirming Larcher and Stockinger's conjecture.