What is the probability of connecting two points ?

Details What is the probability of connecting two points ? What is the probability of connecting two points ?

2006-12-28

arxiv.org/abs/cs/0612142v2

J. Phys. A: Math. Theor. 40 (2007) 14099-14116

Computer Science

Discrete Mathematics

a few critical polynomials are at the end of the .tex source file

Scientific paper

10.1088/1751-8113/40/47/005

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 $0 \leq \rho \leq 1$.

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