Infinite-dimensional stochastic dynamical systems motivated by random matrices and statistical physics

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We have established a general construction theorem and an SDE representation theorem for interacting Brownian motions with 2D Coulomb potentials. We have applied them to the representative random point fields arising from Random Matrix Theory such as Ginibre, Dyson, Bessel random point fields, and have detected and solve the infinite-dimensional stochastic differential equations describing the associated stochastic dynamics. We prove the Palm measures of Ginibre random point field have very strange property that is very different from usual Gibbs measures with Ruelle' s class interaction potentials. We have constructed the time evolutional model of 2D Young diagram and have proved its scaling limit.