分野別セミナー

アブストラクト:
In this talk, we discuss L^{p}-uniqueness of diffusion
operators for Gibbs measures with exponential interaction
potentials on an infinite volume path space
C(¥mathbb R, ¥mathbb R^{d}). We also give an SPDE
characterization of the corresponding dynamics.
In particular, we show existence and uniqueness of
a strong solution for the SPDE, though the interaction
potential is not assumed to be differentiable, hence the
drift is possibly discontinuous. As examples, to which our
results apply, we mention the stochastic quantization of
P(¥phi)_{1}-, exp(¥phi)_{1}-quantum fields in infinite volume.
If time permits, we discuss some functional inequalities
as an application of the uniqueness results. This talk is
based on jointwork with S. Albeverio and M. Roeckner.
※ 今学期のセミナーの開始時刻は午後4時からです．