Percolation and limit theory for the poisson lilypond model. Issue 2 (29th February 2012)

• Record Type: Journal Article
• Authors: Last, Günter; Penrose, Mathew D.
• Is Part Of: Random structures & algorithms. Volume 42:Issue 2(2013)
• Page Start: 226
• Page End: 249
• Publication Date: 2012-02-29
• Subjects: Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20410
• Languages: English
• ISSNs: 1042-9832

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>The lilypond model on a point process in <italic>d</italic> ‐space is a growth‐maximal system of non‐overlapping balls centred at the points. We establish central limit theorems for the total volume and the number of components of the lilypond model on a sequence of Poisson or binomial point processes on expanding windows. For the lilypond model over a homogeneous Poisson process, we give subexponentially decaying tail bounds for the size of the cluster at the origin. Finally, we consider the enhanced Poisson lilypond model where all the balls are enlarged by a fixed amount (the enhancement parameter), and show that for <italic>d</italic> &gt; 1 the critical value of this parameter, above which the enhanced model percolates, is strictly positive. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012</p> </abstract>