演講訊息 TALKS

Abstract: The Kardar-Parisi-Zhang (KPZ) equation is a nonlinear stochastic partial differential equation, which is actually ill-posed because of inconsistency between the nonlinearity and the roughness of the noise. We introduce a renormalization procedure for the KPZ equation, which is appropriate from the view point to identify the invariant measures. The Cole-Hopf transform applied to this approximating equation leads to a linear stochastic heat equation (SHE) with a smeared noise having an extra complex nonlinear term. Under the time average, this complex term can be replaced by a simple linear term, at least under the situation that the corresponding tilt process is stationary. As a result, it is shown that the distribution of a two-sided geometric Brownian motion with a height shift given by Lebesgue measure is invariant under the evolution determined by the SHE.