2006/12/31 by Christian Tanguy
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Continuum percolation theory #Eigenvalues and eigenvectors #Function (biology) #Link (geometry) #Percolation (cognitive psychology) #Polynomial #Product (mathematics) #Random Matrices and Applications #Reliability and Maintenance Optimization #Scaling #Social connectedness #Theoretical and Computational Physics #Transfer (computing) #cs.DM #cs.NI
paper · pdf · doi:10.1088/1751-8113/40/47/005
published as J. Phys. A: Math. Theor. 40 (2007) 14099-14116 · a few critical polynomials are at the end of the .tex source file
openalex publication_date 2007/11/06 · arxiv created 2008/07/03 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 behaviour, 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 ⩽ ρ ⩽ 1.