✦ LIBER ✦
Pairs of graphs with site and bond percolation critical probabilities in opposite orders
✍ Scribed by John C. Wierman
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 181 KB
- Volume
- 129
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
✦ Synopsis
In simulation studies in the physics literature, there is only one pair of graphs which have site and bond percolation critical probability estimates in the opposite order. We prove that this phenomenon does occur, by constructing an inÿnite collection of two-dimensional inÿnite graphs G(n) with the property. The construction will produce such a sequence of graphs in any dimension d ¿ 2.