Kardar-Parisi-Zhang universality class — stochastic growth of an interface
The KPZ equation (Kardar, Parisi, Zhang 1986) describes the stochastic growth of an interface: ∂h/∂t = ν∇²h + (λ/2)(∇h)² + η. The three terms represent: surface tension (smoothing), lateral growth (nonlinearity), and random noise. For λ=0 this reduces to the Edwards-Wilkinson (EW) class. The KPZ scaling exponents are exact in 1D: roughness α=1/2, growth β=1/3, dynamic z=3/2. The KPZ universality class was connected in 2010 to GUE Tracy-Widom fluctuations from random matrix theory — a stunning unexpected link.