Low discrepancy sequences failing Poissonian pair correlations
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DOI: 10.1007/s00013-019-01336-3
Abstract: M. Levin defined a real number x that satisfies that the sequence of the fractional parts of $$(2^n x)_{n\ge 1}$$(2nx)n≥1 are such that the first N terms have discrepancy $$O((\log N)^2/ N)$$O((logN)2/N), which is the… read more here.
Keywords: fractional parts; low discrepancy; pair correlations; poissonian pair ... See more keywords
A note on sequences not having metric Poissonian pair correlations
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DOI: 10.1007/s00013-021-01578-0
Abstract: The purpose of this note is to present a construction of sequences which do not have metric Poissonian pair correlations (MPPC) and whose additive energies grow at rates that come arbitrarily close to a threshold… read more here.
Keywords: sequences metric; metric poissonian; pair correlations; poissonian pair ... See more keywords