The Ising model and percolation on trees and tree-like graphs
β Scribed by Russell Lyons
- Publisher
- Springer
- Year
- 1989
- Tongue
- English
- Weight
- 803 KB
- Volume
- 125
- Category
- Article
- ISSN
- 0010-3616
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The N-cube is a graph with 2 N vertices and N 2 Ny1 edges. Suppose indepen- dent uniform random edge weights are assigned and let T be the spanning tree of minimal Ε½ . y 1 N Ο± y3 total weight. Then the weight of T is asymptotic to N 2 Γ i as N Βͺ Ο±. Asymp-is1 totics are also given for the local stru
Consider independent bond percolation with retention probability p on a Ε½ . spherically symmetric tree β«. Write p for the probability that the root is in an infinite β« Γ Ε½ . 4 Ε½ . open cluster, and define the critical value p s inf p : p ) 0 . If p s 0, then the c β« β« c root may still percolate in t