Scaling Limits of Wick Ordered KPZ Equation

Consider the KPZ equation (u)\dot](t,x)=Du(t,x)+|?u(t,x)|²+W(t,x)\dot u(t,x)=\Delta u(t,x)+|\nabla u(t,x)|^2+W(t,x), x]Â^d, where W(t,x) is a space-time white noise. This paper investigates the question of whether, for some exponents h and z, k^{mh}u(k^z t, kx) converges in some sense as k?￥k\to\infty, and if so, what are the values of these exponents. The non-linear term in the KPZ equation is interpreted as a Wick product and the equation is solved in a suitable space of stochastic distributions. The main tools for establishing the scaling properties of the solution are those of white noise analysis, in particular, the Wiener chaos expansion. A notion of convergence in law in the sense of Wiener chaos is formulated and convergence in this sense of k^{mh}u(k^z t, kx) as kMX is established for various values of h and z depending on the dimension d.