Condensation and Metastable Behavior of Non-reversible Inclusion Processes

In this article, we perform quantitative analyses of metastable behavior an interacting particle system known as the inclusion process. For processes, it is widely believed that nucleates condensation particles because attractive nature interaction mechanism. The processes corresponds to movement condensate on a suitable time scale, and computation corresponding scale characterization scaling limit motion are main problems in study metastability processes. Previously, these were solved for reversible [Bianchi, Dommers, Giardin\`a, Electronic Journal Probability, 22: 1-34, 2017], contribution present extend analysis wide class non-reversible Non-reversibility major obstacle analyzing such models, mainly there no closed-form expression invariant measure general case, our achievement overcome difficulty. particular, results demonstrate limiting process quantitatively qualitatively different from those ones, respectively. We emphasize that, best knowledge, first rigorous when not explicitly known. addition, consider thermodynamic large torus paper [Armend\'ariz, Grosskinsky, Loulakis, Probability Theory Related Fields, 169: 105-175, 2017]. model, observe three scales according level asymmetry model.