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John Wierman

The Johns Hopkins University



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490 – Theory and Foundations

An Improved Upper Bound for the Bond Percolation Threshold of the Cubic Lattice

Sponsor: IMS
Keywords: cubic lattice, bond percolation, percolation threshold, stochastic ordering

John Wierman

The Johns Hopkins University

The bond percolation threshold of the cubic lattice is shown to be less than 0.447792 by applying the approach of Wierman and McCarthy (2015) based on the containment principle and substitution method, but employing a more efficient computational method. The bound is only a slight improvement of the their uppper bound of 0.452595, and the investigation suggests that substantial further improvements are unlikely using this approach.

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