2004/12/31 by Béla Bollobás, Bela Bollobas, Oliver Riordan · 1 citation
Mathematics · #Combinatorics #Continuum percolation theory #Critical exponent #Discrete mathematics #Geometry #Markov Chains and Monte Carlo Methods #Mathematical proof #Mathematics #Percolation (cognitive psychology) #Percolation critical exponents #Percolation theory #Percolation threshold #Physics #Plane (geometry) #Product (mathematics) #Quantum mechanics #Random Matrices and Applications #Statistical physics #Stochastic processes and statistical mechanics #Topology (electrical circuits) #Voronoi diagram #math.CO #math.PR #msc:60K35 #msc:82B43
paper · pdf · doi:10.1002/rsa.20134
published as Random Structures and Algorithms 29 (2006), 524--548. · 28 pages, 8 figures. Minor revisions and additions. To appear in Random Structures and Algorithms
arxiv created 2005/10/04 · openalex publication_date 2006/09/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract Recently, it was shown by Bollobás and Riordan Probab Theory Related Fields 136 (2006), 417–468 that the critical probability for random Voronoi percolation in the plane is 1/2. As a by‐product of the method, a short proof of the Harris–Kesten Theorem was given by Bollobás and Riordan Bull London Math Soc 38 (2006), 470–484 . The aim of this paper is to show that the techniques used in these papers can be applied to many other planar percolation models, both to obtain short proofs of known results and to prove new ones. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006