Percolation Processes. I. Low-Density Expansion for the Mean Number of Clusters in a Random Mixture
- 1 September 1966
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 7 (9) , 1573-1581
- https://doi.org/10.1063/1.1705067
Abstract
A cluster expansion, valid at low densities, is derived for the mean number of clusters in a random mixture of sites or bonds on a graph. It is shown that only clusters without a cut-point (stars) are required, and a number of general theorems for determining the weights are proved.Keywords
This publication has 4 references indexed in Scilit:
- Lattice Constant Systems and Graph TheoryJournal of Mathematical Physics, 1966
- Exact Critical Percolation Probabilities for Site and Bond Problems in Two DimensionsJournal of Mathematical Physics, 1964
- Percolation Processes and Related TopicsJournal of the Society for Industrial and Applied Mathematics, 1963
- Some Cluster Size and Percolation ProblemsJournal of Mathematical Physics, 1961