Kardar-Parisi-Zhang equation: ∂h/∂t = ν∇²h + (λ/2)(∇h)² + η(x,t). The interface width W(t) = std(h) grows as tβ. KPZ: β=1/3. Edwards-Wilkinson (no nonlinear term): β=1/4.
Height Profile
Interface Width W(t) — log-log
KPZ universality class (1986): exact β=1/3 in 1D. Tracy-Widom distribution. Nobel-adjacent work in random matrices, TASEP, last-passage percolation.