2013/12/02 by Neville Ball, N. Ball
Mathematics · Physics and Astronomy · #CDF-based nonparametric confidence interval #Combinatorics #Confidence interval #Electrical resistivity and conductivity #Lattice (music) #Markov Chains and Monte Carlo Methods #Mathematics #Percolation (cognitive psychology) #Percolation threshold #Physics #Quantum mechanics #Robust confidence intervals #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.CO #math.PR #stat.ME
paper · pdf · doi:10.1007/s10955-014-1018-7
arxiv created 2013/12/02 · openalex publication_date 2014/05/16 · arxiv updated 2015/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We extend the method of Balister, Bollobás and Walters for determining rigorous confidence intervals for the critical threshold of two dimensional lattices to three (and higher) dimensional lattices. We describe a method for determining a full confidence interval and apply it to show that the critical threshold for bond percolation on the simple cubic lattice is between 0.2485 and 0.2490 with 99.9999% confidence, and the critical threshold for site percolation on the same lattice is between 0.3110 and 0.3118 with 99.9999% confidence.