The KPZ equation describes a growing interface with diffusion, nonlinear tilt term, and noise:
∂h/∂t = ν∇²h + (λ/2)(∇h)² + η(x,t)
KPZ universality class is characterized by three critical exponents:
roughness α = 1/2, growth β = 1/3, dynamic z = 3/2.
The interface width scales as W ~ t^β at early times.
The height distribution converges to the Tracy–Widom GUE distribution (not Gaussian!).
Set λ = 0 for Edwards–Wilkinson (EW) class with β = 1/4.