Scaling limits of Wick ordered KPZ equation
The author considers the Kardar-Parisi-Zhang (KPZ) equation [Phys. Rev. Lett. 56, 889-892 (1984)], which is \[ \frac{\partial u}{\partial t}=\nu\Delta u+\frac{\lambda}{2}|\nabla u|^2+\sigma W(t,x),\qquad u(0,x)=u_0(x), \] where \(W(t,x)\) is a space-time white noise, \(u=u(t,x)\) and \(x\in \mathbb{R}^d\). The paper investigates the convergence of rescaled functions of the form \(k^{-\chi}u(k^zt,kx)\), as \(k\to\infty\), for some exponents \(\chi\) and \(z\). This problem is solved for various values of \(\chi\) and \(z\) (depending on the dimension \(d\)) using the Wiener chaos expansion and the tools of white noise analysis.
scientific article; zbMATH DE number 1422935