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 pc. 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 pc. Finally, a Monte Carlo simulation technique is presented; the use thereof establishes 0.64450 as a non-rigorous five-digit-precision (lower) estimate for pc.
Key WordsOriented percolation Discrete time contact processes Critical probability Edge process Markov chain in a strip Coupling Simulation
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