# Full Poissonian Local Statistics of Slowly Growing Sequences

@inproceedings{Lutsko2022FullPL, title={Full Poissonian Local Statistics of Slowly Growing Sequences}, author={Christopher Lutsko and Niclas Technau}, year={2022} }

Fix α > 0, then by Fejér’s theorem (α(logn) mod 1)n≥1 is uniformly distributed if and only if A > 1. We sharpen this by showing that all correlation functions, and hence the gap distribution, are Poissonian provided A > 1. This is the first example of a deterministic sequence modulo one whose gap distribution, and all of whose correlations are proven to be Poissonian. The range of A is optimal and complements a result of Marklof and Strömbergsson who found the limiting gap distribution of (log…

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