Phase transitions for a planar quadratic contact process

We study a two dimensional version of Neuhauser's long range sexual reproduction model and prove results that give bounds on the critical values λf for the process to survive from a finite set and λe for the existence of a nontrivial stationary distribution. Our first result comes from a standard block construction, while the second involves a comparison with the “generic population model” of Bramson and Gray (1991) [3]. An interesting new...