Brownian Paths Homogeneously Distributed in Space: Percolation Phase Transition and Uniqueness of the Unbounded Cluster

Dirk Erhard, Julián Martínez, Julien Poisat

We consider a continuum percolation model on ${\mathbb{R}}^d$, $d\ge 1$.For $t,\lambda \in (0,\infty )$ and $d\in \{1,2,3\}$, the occupied set is given by the union of independent Brownian paths run…