What is the probability of connecting two points ?
Christian Tanguy
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 ≤ ρ≤ 1.
Create a lesson
Related papers
The Project Scheduling Interdiction Problem with Delay Groups
Fei Wu, Erik Demeulemeester, Jannik Matuschke
Rank-Three Projections and Minimal Multiplicity Bipartitions of Path Complements
Jintao Fei, Jiangying Luo
Faster FPRAS for the Permanent via Restricted Poincaré Inequalities and Coupled Flows
Xiaoyu Chen, Eric Vigoda, Xiongxin Yang
On identifying codes on oriented graphs
Soura Sena Das, Sagnik Sen
Parallelizable Gradient-Based Optimization For Multi-Objective MaxCut
Jingjuan Huang, Alvaro Velasquez, Jia Liu et al.
Algebraic Characterizations for Minors of Finite Graphs via Flow Transformation Monoid Division and Embedding
Amena Assem, Hanna Derets, Chrystopher L. Nehaniv