1990/08/08 by Geoffrey Grimmett, J. M. Marstrand · 4 citations
Mathematics · Psychology · #Stochastic processes and statistical mechanics #Mathematical Dynamics and Fractals #Markov Chains and Monte Carlo Methods #Supercritical fluid #Percolation critical exponents #Percolation (cognitive psychology) #Percolation threshold #Statistical physics #Directed percolation #Mathematics #Continuum percolation theory #Lattice (music) #Phase transition #Critical exponent #Physics #Condensed matter physics #Thermodynamics #Quantum mechanics #Electrical resistivity and conductivity #Psychology
paper · doi:10.1098/rspa.1990.0100
openalex publication_date 1990/08/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/06/26
Abstract We prove a general result concerning the critical probabilities of subsets of a lattice L. It is a consequence of this result that the critical probability of a percolation process on L equals the limit of the critical probability of a slice of L as the thickness of the slice tends to infinity. This verification of one of the standard hypotheses of the subject settles many questions concerning supercritical percolation.