Inserted: 16 sep 2008
Last Updated: 24 nov 2008
We study some percolation problems on the complete graph over $\mathbf N$. In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the probability, such as independency, is made.
The main tools are a topological version of Ramsey theory, exchangeability theory and elementary ergodic theory.