Extremal-point densities of interface fluctuations

We introduce and investigate the stochastic dynamics of the density of loca l extrema (minima and maxima) of nonequilibrium surface fluctuations. We gi ve a number of analytic results for interface fluctuations described by lin ear Langevin equations, and for an-lattice, solid-on-solid surface-growth m odels. We show that, in spite of the nonuniversal character of the quantiti es studied, their behavior against the variation of the microscopic length scales can present generic features, characteristic of the macroscopic obse rvables of the system. The quantities investigated here provide us with too ls that give an unorthodox approach to the dynamics of surface morphologies : a statistical analysis from the short-wavelength end of the Fourier decom position spectrum. In addition to surface-growth applications, our results can be used to solve the asymptotic scalability problem of massively parall el algorithms for discrete-event simulations, which are extensively used in Monte Carlo simulations on parallel architectures.