Additive energy, discrepancy and Poissonian $k$-level correlation

Autor:	Lachman, Guy, Regavim, Shvo
Rok vydání:	2021
Předmět:	Mathematics - Number Theory Mathematics - Probability 11K38 11K06
Druh dokumentu:	Working Paper
Popis:	$k$-level correlation is a local statistic of sequences modulo 1, describing the local spacings of $k$-tuples of elements. For $k = 2$ this is also known as pair correlation. We show that there exists a well spaced increasing sequence of reals with additive energy of order $N^3$ and Poissonian $k$-level correlation for all integers $k \geq 2$, answering in the affirmative a question raised by Aistleitner, El-Baz, and Munsch. The construction is probabilistic, and so we do not obtain a specific sequence satisfying this condition. To prove this, we show that random perturbations of a sequence with small discrepancy gives, almost surely, a sequence with Poissonian $k$-level correlation, a fact which may be of independent interest. Comment: 11 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2109.05379 Zobrazit plný text záznamu View this record from Arxiv