A Harris‐Kesten theorem for confetti percolation1. Issue 2 (4th August 2014)

• Record Type: Journal Article
• Authors: Hirsch, Christian
• Is Part Of: Random structures & algorithms. Volume 47:Issue 2(2015)
• Page Start: 361
• Page End: 385
• Publication Date: 2014-08-04
• Subjects: Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20563
• Languages: English
• ISSNs: 1042-9832

Abstract

<abstract abstract-type="main"> <title>ABSTRACT</title> <p>Percolation properties of the dead leaves model, also known as confetti percolation, are considered. More precisely, we prove that the critical probability for confetti percolation with square‐shaped leaves is 1/2. This result is related to a question of Benjamini and Schramm concerning disk‐shaped leaves and can be seen as a variant of the Harris‐Kesten theorem for bond percolation. The proof is based on techniques developed by Bollobás and Riordan to determine the critical probability for Voronoi and Johnson‐Mehl percolation. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 361–385, 2015</p> </abstract>