A universal law for Voronoï cell volumes in infinitely large maps. (8th January 2018)

• Record Type: Journal Article
• Authors: Guitter, Emmanuel
• Is Part Of: Journal of statistical mechanics. (2018:Jan.)
• Publication Date: 2018-01-08
• Subjects: 11 -- 1; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aa9db4
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We discuss the volume of Voronoï cells defined by two marked vertices picked randomly at a fixed given mutual distance 2 s in random planar quadrangulations. We consider the regime where the mutual distance 2 s is kept finite while the total volume of the quadrangulation tends to infinity. In this regime, exactly one of the Voronoï cells keeps a finite volume, which scales as s 4 for large s . We analyze the universal probability distribution of this, properly rescaled, finite volume and present an explicit formula for its Laplace transform.