Fluctuation Exponent of the Kpz/stochastic Burgers Equation

(1.4) hε(t, x) = ε 1/2h(ε−zt, ε−1x). We will be considering these models in equilibrium, in which case h(t, x)−h(t, 0) is a two-sided Brownian motion with variance ν−1σ2 for each t. There are many physical arguments for (1.3), none of which are good starting points for rigorous analysis, and which are really only convincing in the sense that they are very well backed up by numerical work. Perhaps the simplest is to note that the rescaling εh(·, ε−1x)