Approximate upper bounds for the critical probability of oriented percolation in two dimensions based on rapidly mixing Markov chains
Authors:
- Béla BollabásBBBéla Bollabás
- Alan StaceyASAlan Stacey
- 1 December 1997
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 34 (4) , 859-867
Abstract
We develop a technique for establishing statistical tests with precise confidence levels for upper bounds on the critical probability in oriented percolation. We use it to givepc< 0.647 with a 99.999967% confidence. As Monte Carlo simulations suggest thatpc≈ 0.6445, this bound is fairly tight.Keywords
This publication has 11 references indexed in Scilit:
- Survival of Discrete Time Growth Models, with Applications to Oriented PercolationThe Annals of Applied Probability, 1995
- Improved upper bounds for the critical probability of oriented percolation in two dimensionsRandom Structures & Algorithms, 1994
- Upper bounds for the critical probability of oriented percolation in two dimensionsProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1993
- Stochastic growth models: bounds on critical valuesJournal of Applied Probability, 1992
- Percolation1989
- The critical probability of bond percolation on the square lattice equals 1/2Communications in Mathematical Physics, 1980
- A note on percolationProbability Theory and Related Fields, 1978
- Percolation Probabilities on the Square Lattice1978
- A lower bound for the critical probability in a certain percolation processMathematical Proceedings of the Cambridge Philosophical Society, 1960
- Percolation processesMathematical Proceedings of the Cambridge Philosophical Society, 1957