KPZ Stochastic Interface Growth

Kardar–Parisi–Zhang universality class — roughness exponents & Tracy-Widom fluctuations
ν (diffusion) 1.0
λ (nonlinear) 1.0
D (noise) 1.0
W = —
β ≈ —
The KPZ equation ∂h/∂t = ν∇²h + (λ/2)(∇h)² + η describes stochastic interface growth. The roughness W(t) ~ tβ with β = 1/3 in 1+1D (KPZ universality). Height fluctuations in the stationary state follow the Tracy-Widom GUE distribution.