Metric Poissonian pair correlation for real sequences and energy estimates

TL;DR

This paper introduces new conditions ensuring that real sequences exhibit metric Poissonian pair correlation, strengthening previous results and resolving an open problem, with applications to convex and polynomial sequences.

Contribution

It provides novel conditions for metric Poissonian pair correlation and applies them to specific classes of sequences, advancing the understanding of their statistical properties.

Findings

Established new conditions for metric Poissonian pair correlation.

Resolved an open problem under mild growth assumptions.

Showed convex and polynomial sequences have metric Poissonian pair correlation.

Abstract

We establish new conditions under which a sequence of real numbers has metric Poissonian pair correlation. These conditions strengthen results of Aistleitner, El-Baz and Munsch (2021) and resolve one of their open problems under a mild growth assumption. As applications, we show that quantitatively convex and polynomial sequences have metric Poissonian pair correlation.