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What is the probability of connecting two points ?

Christian Tanguy
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Abstract

The two-terminal reliability, known as the pair connectedness or connectivity function in percolation theory, may actually be expressed as a product of transfer matrices in which the probability of operation of each link and site is exactly taken into account. When link and site probabilities are $p$ and $ρ$, it obeys an asymptotic power-law behavior, for which the scaling factor is the transfer matrix's eigenvalue of largest modulus. The location of the complex zeros of the two-terminal reliability polynomial exhibits structural transitions as $0 \leq ρ\leq 1$.

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Christian Tanguy. 2008-07-03. What is the probability of connecting two points ?. https://doi.org/10.1088/1751-8113/40/47/005

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