Generalized immediate exchange models and their symmetries

TL;DR

This paper introduces a generalized class of immediate exchange models involving mass splitting, exchange, and merging, revealing symmetries and self-duality properties through connections to well-known stochastic processes.

Contribution

It extends the immediate exchange model by incorporating broader splitting mechanisms and establishes their symmetries via relations to symmetric inclusion, exclusion, and independent random walk processes.

Findings

Identifies symmetries and self-duality in generalized models

Connects splitting processes to symmetric inclusion and exclusion processes

Demonstrates analogous properties across different stochastic models

Abstract

We reconsider 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 of the generalized IEM model. We show that analogous properties hold for models were the splitting is related to the symmetric exclusion process or to independent random walkers.