One-dimensional Kardar-Parisi-Zhang and Kuramoto-Sivashinsky universality class: Limit distributions
One-dimensional Kardar-Parisi-Zhang and Kuramoto-Sivashinsky universality class: Limit distributions
Tracy-Widom and Baik-Rains distributions appear as universal limit distributions for height fluctuations in the one-dimensional Kardar-Parisi-Zhang (KPZ) stochastic partial differential equation (PDE). We obtain the same universal distributions in the spatiotemporally chaotic, nonequilibrium, but statistically steady state of the one-dimensional Kuramoto-Sivashinsky (KS) deterministic PDE, by carrying out extensive pseudospectral direct …