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.
- R. Durrett, Oriented Percolation in Two Dimensions. The Annals of Probability 12(4):999–1040 (1984).
- R. Durrett, Lecture Notes on Particle Systems and Percolation. Wadsworth & Brooks/Cole (1988).
- G. Grimmett, Percolation. Springer Verlag (1999).
- G. Fayolle, V.A. Malyshev, M.V. Menshikov, Topics in the Constructive Theory of Countable Markov Chains. Cambridge University Press (1995).
- R. G. Bartle, The Elements of Integration and Lebesgue Measure. John Willey & Sons Inc (1995).
- J. H. Wilkinson, Rounding Errors in Algebraic Processes. Her Majesty's Stationary Office (1963).
- 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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