Sequences modulo one: convergence of local statistics

Abstract

We survey recent results beyond equidistribution of sequences modulo one. We focus on the sequence of angles in a Euclidean lattice in ${\mathbb{R}}^2$ and on the sequence $\sqrt{n}\mathrm{mod}1$.

arXiv comment6 figures. arXiv admin note: text overlap with arXiv:1306.0028

References in corpus (3)

• Gaps between logs
• Uniqueness of the measure of maximal entropy for the squarefree flow
• Effective Ratner theorem for ASL(2,R) and gaps in \sqrt{n} modulo 1