Work

On Sequences With Exponentially Distributed Gaps

Year: 2024

Type: article

Abstract: ABSTRACT It is well known that a sequence which has Poissonian correlations of all orders necessarily has exponentially distributed nearest‐neighbor gaps. It is natural to ask whether this implication also holds in the other direction, that is, whether a sequence with exponential gap distribution must have Poissonian correlations, and by an already known fact, must be equidistributed. We show that this assertion is generally false, by constructing a sequence that has exponential gap distribution but fails to be equidistributed (and as a consequence, also fails to have Poissonian correlations of any order and scale).

Source: Random Structures and Algorithms

DOI: 10.1002/rsa.21265

Authors: Christoph Aistleitner, Manuel Hauke, Agamemnon Zafeiropoulos

Institutions: Graz University of Technology, University of York, Technion – Israel Institute of Technology

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,330

Funders: Austrian Science Fund, Engineering and Physical Sciences Research Council, H2020 European Research Council