THE 3-POINT CORRELATION-FUNCTION IN AN ENSEMBLE OF 3-DIMENSIONAL SIMULATIONS

We evaluate the three-point function in Fourier space for an ensemble of three-dimensional 128(3) numerical simulations with initial power s pectra characterized by spectral index n = +1, 0, -1, -2, -3, with no high-frequency cutoff and with cutoff k(c) = 16 or k(c) = 4. To remove dependences on scale and on time, we present results as the reduced a mplitude Q in the hierarchical model as a function of the dimensionles s variable kd(rms), where d(rms) is the mean square displacement of a particle from its initial position. For scale-free initial conditions, there is no evolution in Q. For initial conditions with a cutoff, Q e volves until the scale of the cutoff is in the nonlinear regime; the r esults afterwards are no different from those with no initial cutoff. We are able to follow, for the first time, the transition from quasi-l inear to nonlinear regimes. In the quasi-linear regime, our results ag ree well with gravitational perturbation theory predictions, including a marked dependence on the shape of the configuration. In the nonline ar regime, the value of Q for scale-invariant initial conditions is re markably independent of evolution epoch, of scale, and of configuratio n shape, and depends on spectral index roughly as Q = 3/(3 + n).