Extrema statistics in the dynamics of a non-Gaussian random field
  When the equations that govern the dynamics of a random field are nonlinear,
the field can develop with time non-Gaussian statistics even if its initial
condition is Gaussian. Here, we provide a general framework for calculating the
effect of the underlying nonlinear dynamics on the relative densities of maxima
and minima of the field. Using this simple geometrical probe, we can identify
the size of the non-Gaussian contributions in the random field, or
alternatively the magnitude of the nonlinear terms in the underlying equations
of motion. We demonstrate our approach by applying it to an initially Gaussian
field that evolves according to the deterministic KPZ equation, which models
surface growth and shock dynamics.
