Phase transitions for the Widom--Rowlinson model in random environments

We establish non-uniqueness regimes for the infinite-volume two-colored Widom–Rowlinson model based on inhomogeneous Poisson point processes with locally finite intensity measures featuring percolation. As an application, we provide almost-sure phase-transition results for the Widom–Rowlinson model based on translation-invariant and ergodic Cox point processes with stabilizing and non-stabilizing directing measures.