, Volume 122, Issue 2, pp 279-302

Improved Lower Bounds for the Critical Probability of Oriented Bond Percolation in Two Dimensions

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Abstract

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.

Mathematics Subject Classification (1991): 60K35
Supported by CNPq (grant N.301637/91-1).
Supported by a grant from CNPq.