Abstract
We consider Bernoulli percolation on a locally finite quasi-transitive unimodular graph and prove that two infinite clusters cannot have infinitely many pairs of vertices at distance 1 from one another or, in other words, that such graphs exhibit "cluster repulsion." This partially answers a question of Häggström, Peres and Schonmann.
| Original language | English |
|---|---|
| Pages (from-to) | 2332-2343 |
| Number of pages | 12 |
| Journal | Annals of Probability |
| Volume | 34 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - Nov 2006 |
Other keywords
- Cluster repulsion
- Nonamenable
- Percolation
- Touching clusters