Kardar–Parisi–Zhang equation

In mathematics, the Kardar–Parisi–Zhang (KPZ) equation is a non-linear stochastic partial differential equation, introduced by Mehran Kardar, Giorgio Parisi, and Yi-Cheng Zhang in 1986. It describes the temporal change of a height field h ( x → , t ) {displaystyle h({vec {x}},t)} with spatial coordinate x → {displaystyle {vec {x}}} and time coordinate t {displaystyle t} : In mathematics, the Kardar–Parisi–Zhang (KPZ) equation is a non-linear stochastic partial differential equation, introduced by Mehran Kardar, Giorgio Parisi, and Yi-Cheng Zhang in 1986. It describes the temporal change of a height field h ( x → , t ) {displaystyle h({vec {x}},t)} with spatial coordinate x → {displaystyle {vec {x}}} and time coordinate t {displaystyle t} : Here η ( x → , t ) {displaystyle eta ({vec {x}},t)} is white Gaussian noise with average ⟨ η ( x → , t ) ⟩ = 0 {displaystyle langle eta ({vec {x}},t) angle =0}