Quasi-reversible Creation-annihilation Models: Colliding Bullet Model with Creations and a Loop Model
Jérôme Casse
2026, v.32, Issue 3, 261-300
ABSTRACT
We consider a large class of creation-annihilation models that contains, in particular, the colliding bullet model with creations and a loop model. For this large class of creation-annihilation models, we give sufficient conditions on their parameter to be rot(π)-quasi-reversible and to be rot(π/2)-quasi-reversible. Moreover, those conditions assure them that one of their stationary measures is described by a Poisson point process. These results, applied to the colliding bullet model with creations, are the first steps to study its non-empty stationary measure, and, applied to the loop model, prove its invariance according to all the symmetries of the square.
doi:10.61102/1024-2953-mprf.2026.32.3.001
Keywords: Dynamical systems, invariant measure, quasi-reversibility
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