Asymptotic Expansion of the One-Loop Approximation of the Chern-Simons Integral in an Abstract Wiener Space Setting

In an abstract Wiener space setting, we constract a rigorous mathematical model of the one-loop approximation of the perturbative Chern-Simons integral, and derive its explicit asymptotic expansion for stochastic Wilson lines.Comment: 39 page

Comparison and nuclearity of spaces of differential forms on topological vector spaces

Two types of fundamental spaces of differential forms on infinite dimensional topological vector spaces are considered; one is a fundamental space of Hida's type and the other is one of Malliavin's. It is proven that the former space is smaller than the latter. Moreover, it is shown that, under some conditions, the fundamental space of Hida's type is nuclear as a complete countably normed space, while that of Malliavin's in the L2 sense is not

Tightness problem and stochastic evolution equation arising from fluctuation phenomena for interacting diffusions

The central limit (or fluctuation) phenomena are discussed in the interacting diffusion system. The tightness in the Kolmogorov-Prokhorov sense is proved for a sequence of distribution valued processes arising from finite particle systems. Further, the stochastic differential equation for the limit process is derived by constructing an infinite dimensional Brownian motion.central limit theorem fluctuation interacting diffusion system infinite dimensional process