Characterization of the support for Wick powers of the additive stochastic heat equation

Abstract

Let $Z$ be the stationary solution of the additive stochastic heat equation ${\partial }_{t}Z=(\Delta -1)Z+\xi$ on the two-dimensional torus, where $\xi$ is the space-time white noise. The aim of this paper is to determine the support of Wick powers $\{Z^{:k:}{\}}_{k=1}^{\infty }$. This leads to an elementary proof of a support theorem for the dynamic $P(\Phi {)}_2$ equation. In addition, we show that the approach can be used to determine the support of the law of the Gaussian multiplicative chaos in the $L^2$-phase.

arXiv comment29 pages

References in corpus (4)

• Stochastic quantization associated with the $\exp (\Phi {)}_2$-quantum field model driven by space-time white noise on the torus
• The support of singular stochastic PDEs
• Global well-posedness for the two-dimensional stochastic complex Ginzburg-Landau equation
• Global well-posedness of the two-dimensional stochastic complex Ginzburg-Landau equation with cubic nonlinearity

Cited by in corpus (1)

• Global well-posedness of the two-dimensional stochastic complex Ginzburg-Landau equation with cubic nonlinearity