Inhomogeneous exponential jump model

Understand

We introduce and study the inhomogeneous exponential jump model - an integrable stochastic interacting particle system on the continuous half line evolving in continuous time.

• An important feature of the system is the presence of arbitrary spatial inhomogeneity on the half line which does not break the integrability.
• We completely characterize the macroscopic limit shape and asymptotic fluctuations of the height function (= integrated current) in the model.
• In particular, we explain how the presence of inhomogeneity may lead to macroscopic phase transitions in the limit shape such as shocks or traffic jams.