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We prove the sets of polynomials on configuration spaces are cores ofDirichlet forms describing interacting Brownian motion in infinite dimensions.Typical examples of these stochastic dynamics are Dyson's Brownian motion andAiry interacting Brownian motion. Both particle systems have logarithmicinteraction potentials, and naturally arise from random matrix theory. Theresults of the present paper will be used in a forth coming paper to prove theidentity of the infinite-dimensional stochastic dynamics related to the randommatrix theories constructed by apparently different methods: the method ofspace-time correlation functions and that of stochastic analysis.

Cores of Dirichlet forms related to random matrix theory