Abstract
We propose a method of studying the continuous percolation of aligned objects as a limit of a corresponding discrete model. We show that the convergence of a discrete model to its continuous limit is controlled by a power-law dependency with a universal exponent . This allows us to estimate the continuous percolation thresholds in a model of aligned hypercubes in dimensions with accuracy far better than that attained using any other method before. We also report improved values of the correlation length critical exponent ν in dimensions d = 4,5 and the values of several universal wrapping probabilities for .
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