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Approximate upper bounds for the critical probability of oriented percolation in two dimensions based on rapidly mixing Markov chains

Part of: Graph theory Special processes

Published online by Cambridge University Press:  14 July 2016

Béla Bollabás  and
Alan Stacey
Béla Bollabás*
Affiliation:
Cambridge University
Alan Stacey*
Affiliation:
Cambridge University
*
∗Postal address: Department of Pure Mathematics and Mathematical Statistics, Cambridge University, 16 Mill Lane, Cambridge, UK.
∗Postal address: Department of Pure Mathematics and Mathematical Statistics, Cambridge University, 16 Mill Lane, Cambridge, UK.
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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 give pc < 0.647 with a 99.999967% confidence. As Monte Carlo simulations suggest that pc ≈ 0.6445, this bound is fairly tight.

Keywords

PERCOLATIONRAPID MIXINGCOUPLINGCOMPUTER ALGORITHM

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 05C80: Random graphs
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 4 , December 1997 , pp. 859 - 867
Copyright
Copyright © Applied Probability Trust 1997 

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