Fluctuations in an Evolutional Model of Two-Dimensional Young Diagrams

We discuss the non-equilibrium fluctuation problem, which corresponds to the hydrodynamic limit established in \cite{FS}, for the dynamics of two-dimensional Young diagrams associated with the uniform and restricted uniform statistics, and derive linear stochastic partial differential equations in the limit. We show that their invariant measures are identical to the Gaussian measures which appear in the fluctuation limits in the static situations.