On the metric Poissonian pair correlation of real sequences

3:00pm, Wednesday 28th May

Abstract

The Poissonian pair correlation is a local statistic that captures strong pseudo-randomness in deterministic sequences. In a forthcoming paper (potentially on arXiv by the talk), joint work with Bryce Kerr, we provide new sufficient conditions under which a real sequence exhibits the metric Poissonian property. Moreover, our criterion refines and improves existing quantitative bounds on the energy estimates that govern such behaviour. As an application of our results, we show that both convex and polynomial sequences are metric Poissionian.