Pierre Houdebert: Sharp phase transition for the Widom-Rowlinson model

Abstract :
The Widom-Rowlinson model is formally defined as two homogeneous Poisson point processes 
forbidding the points of different type to be too close. For this Gibbs model the question 
of uniqueness/ non-uniqueness depending on the two intensities is relevant. This model is 
famous because it was the first continuum Gibbs model for which phase transition was proven, 
in the symmetric case of equal intensities large enough. But nothing was known in the 
non-symmetric case, where it is conjectured that uniqueness would hold.

In a recent work with D. Dereudre (Lille), we partially solved this conjecture, proving that 
for large enough activities the phase transition is only possible in the symmetric case of equal 
intensities. The proof uses percolation and stochastic domination arguments.