Quasi-reversible bullet models: colliding bullet model with creations and a new(?) loop model

TL;DR

This paper analyzes a broad class of bullet models, including the colliding bullet model with creations and a new loop model, providing conditions for their quasi-reversibility and stationary measures, with implications for symmetry and invariance.

Contribution

It introduces sufficient conditions for quasi-reversibility and stationary measures in a large class of bullet models, including new results for the loop model and colliding bullet models with creations.

Findings

Conditions for $ ext{rot}(\pi)$-quasi-reversibility

Conditions for $ ext{rot}(\pi/2)$-quasi-reversibility

Stationary measures described by Poisson point processes

Abstract

We consider a large class of bullet models that contains, in particular, the colliding bullet model with creations and a new loop model. For this large class of bullet models, we give sufficient conditions on their parameter to be $\text{rot}(\pi)$-quasi-reversible and to be $\text{rot}(\pi/2)$-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.