Generalized immediate exchange models and their symmetries

We reconsider the discrete dual of the immediate exchange model and define a more general class of models where mass is split, exchanged and merged. We relate the splitting process to the symmetric inclusion process via thermalization and from that obtain symmetries and self-duality for it and its generalization. We show that analogous properties hold for models where the splitting is related to the symmetric exclusion process or to independent random walkers. (C) 2017 Elsevier B.V. All rights reserved.