Poissonian pair correlation for higher dimensional real sequences

Abstract In this article, we examine the Poissonian pair correlation (PPC) statistic for higher dimensional real sequences. Specifically, we demonstrate that for , almost all , the sequence in has PPC conditionally on the additive energy bound of . This bound is more relaxed compared to the additive energy bound for one dimension as discussed in [Aistleitner, El‐Baz, and Munsch, Geom. Funct. Anal. 31 (2021), 483–512]. More generally, we derive the PPC for for almost all . As a consequence we establish the metric PPC for provided that all of the are greater than two.