Panagiotis Spanos

Spread out percolation in 2-step nilpotent groups

A simple case of a spread-out percolation on Z^d could be described as follows: for each two points at distance at most $r>0$, we connect them with probability p. A result by Penrose states that as $r/rightarrow /infty$ the critical value of the average degree, for the existence of an infinite component, tends to 1. In this talk we present a generalisation of this model on a finitely generated 2-step nilpotent group. We show that for a specific generator set, the same result applies for its corresponding Cayley graph.