The (d+1)-dimensional KPZ equation \[ \partial_t h = \nu \Delta h + \frac{\lambda}{2}|\nabla h|^2 + \sqrt{D}\dot{W}, \] in which \dot{W} is a space--time white noise, is a natural model for the growth of d-dimensional random surfaces. These surfaces are extremely rough due to the white noise forcing, which leads to difficulties in interpreting the nonlinear term in the equation. In...