Stochastic analysis on large scale interacting systems

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We have studied large scale interacting systems related to the interface model and the theory of random matrices, based on the stochastic analysis and the theory of nonlinear partial differential equations. In particular, concerning the interface model on a wall or with a pinning effect, we have made a precise analysis and determined the scaling limit when the corresponding large deviation rate functional admits plural minimizers, and moreover, established the hydrodynamic limit for an evolutional model of two dimensional Young diagrams. As a dynamic model in the theory of random matrices, we have investigated the system of Ginibre interacting Brownian particles and found an outstanding property, that is, the sub-diffusive behavior of a tagged particle in this system.