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.