Stretched exponential decay of correlations in the quasiperiodic continuum percolation model

We study the continuum percolation model, which is defined on ${\mathbb{Z}}^d\times \mathbb{R}$ so that the connections in the continuous directions are not oriented in time, with quasiperiodically disordered fields. The oriented version of the model is the contact process. We consider intermediate strengths of disorder of the fields and show stretched exponential decay of correlations.