On Inhomogeneous Poissonian Pair Correlations

TL;DR

This paper investigates inhomogeneous Poissonian pair correlations, revealing that such sequences can lack uniform distribution, which challenges previous assumptions and enhances understanding of their properties.

Contribution

It introduces and analyzes inhomogeneous Poissonian pair correlations, demonstrating that these sequences need not be uniformly distributed, contrary to prior beliefs.

Findings

Sequences with inhomogeneous Poissonian pair correlations are not necessarily uniformly distributed.

The paper establishes properties showing similarities and differences to homogeneous Poissonian correlations.

It challenges the previous assumption that such sequences must be uniformly distributed.

Abstract

We study the notion of inhomogeneous Poissonian pair correlations, proving several properties that show similarities and differences to its homogeneous counterpart. In particular, we show that sequences with inhomogeneous Poissonian pair correlations need not be uniformly distributed, contrary to what was till recently believed.