Corners and Records of the Poisson Process in Quadrant

2007/09/09 by Alexander Gnedin, Gnedin, Alexander
Mathematics · #60G55 #60G70 #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematical functions and polynomials #Probability (math.PR) #math.PR #msc:60G55 #msc:60G70

paper · pdf · doi:10.48550/arxiv.0709.1285

6 pages

arxiv created 2007/09/09 · openalex publication_date 2007/09/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The scale-invariant spacings lemma due to Arratia, Barbour and Tavaré establishes the distributional identity of a self-similar Poisson process and the set of spacings between the points of this process. In this note we connect this result with properties of a certain set of extreme points of the unit Poisson process in the positive quadrant.

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