This paper studies a particle model connected to a Pieri-type formula for the symplectic compact group. Particles evolve independently apart from a blocking and pushing interaction such that they remain in the set of symplectic Gelfand-Tsetlin patterns. We show that if only one row of the patterns is considered, one obtains a symplectic Schur process. The model leads in particular to the particle model with a wall defined by Jon Warren and Peter Windridge and to a matrix model previously studied by the author.
"Interacting particle models and the Pieri-type formulas: the symplectic case with non equal weights." Electron. Commun. Probab. 17 1 - 12, 2012. https://doi.org/10.1214/ECP.v17-2193