What is the probability of connecting two points ?
<|reference_start|>What is the probability of connecting two points ?: 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 $\rho$, 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 $0 \leq \rho \leq 1$.<|reference_end|>
@article{tanguy2006what,
    title={What is the probability of connecting two points ?},
    author={Christian Tanguy},
    journal={J. Phys. A: Math. Theor. 40 (2007) 14099-14116},
    year={2006},
    doi={10.1088/1751-8113/40/47/005},
    archivePrefix={arXiv},
    eprint={cs/0612142},
    primaryClass={cs.DM cs.NI}
}