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

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

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Article ID: iaor1999346
Country: United Kingdom
Volume: 34
Issue: 4
Start Page Number: 859
End Page Number: 867
Publication Date: Dec 1997
Journal: Journal of Applied Probability
Authors: ,
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.

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