We introduce and study a new interacting particles model with a wall and two kinds of interactions - blocking and pushing - which maintain particles in a certain order. We show that it involves a random matrix model.
"Generalized Laguerre Unitary Ensembles and an interacting particles model with a wall." Electron. Commun. Probab. 16 59 - 69, 2011. https://doi.org/10.1214/ECP.v16-1602