Rigorous confidence intervals for critical probabilities

Details Rigorous confidence intervals for critical probabilities Rigorous confidence intervals for critical probabilities

2007-02-08

arxiv.org/abs/math/0702232v1

Physical Review E 76, 011110 (2007)

Mathematics

Probability

Scientific paper

10.1103/PhysRevE.76.011110

We use the method of Balister, Bollobas and Walters to give rigorous 99.9999% confidence intervals for the critical probabilities for site and bond percolation on the 11 Archimedean lattices. In our computer calculations, the emphasis is on simplicity and ease of verification, rather than obtaining the best possible results. Nevertheless, we obtain intervals of width at most 0.0005 in all cases.

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