Improved Lower Bounds for the Critical Probability of Oriented Bond Percolation in Two Dimensions
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We present a coupled decreasing sequence of random walks on Z that dominate the edge process of oriented bond percolation in two dimensions. Using the concept of random walk in a strip, we describe an algorithm that generates an increasing sequence of lower bounds that converges to the critical probability of oriented percolation p c. From the 7th term on, these lower bounds improve upon 0.6298, the best rigorous lower bound at present, establishing 0.63328 as a rigorous lower bound for p c. Finally, a Monte Carlo simulation technique is presented; the use thereof establishes 0.64450 as a non-rigorous five-digit-precision (lower) estimate for p c.
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- Improved Lower Bounds for the Critical Probability of Oriented Bond Percolation in Two Dimensions
Journal of Statistical Physics
Volume 122, Issue 2 , pp 279-302
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- Kluwer Academic Publishers-Plenum Publishers
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- Oriented percolation
- Discrete time contact processes
- Critical probability
- Edge process
- Markov chain in a strip
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