Stochastic analysis on infinite-dimensional stochastic differential equations related to random matrices (Mathematical aspects of quantum fields and related topics)

Abstract

This is an article for announcement of our papers [8, 10, 11]. We consider dynamics associated with random point fields with infinitely many particles. The dynamics is introduced through Dirichlet form theory, and it can be represented by infinitedimensional stochastic differential equation (ISDE). In particular, we treat infinite particle systems with long-range interaction, which naturally appear in random matrix theory.