Nonlinear Evolution of Topologyof Large Scale Structure

As a statistical measure of large-scale structure of the universe, the genus number is presented in analytic form for realistic non-Gaussian distributions, i.e., weakly non-Gaussian, lognormal and chi-square distributions. These formulae are compared with the results of N-body simulation. It is shown that the weakly non-Gaussian formula describes the behavior of genus in weakly nonlinear regime fairly accurately and that the lognormal formula ts the simulation data the best in mildly nonlinear regime. We conclude that if analytic formulae and direct numerical simulations are combined, the normalized genus curve G()=G(0) is a powerful tool to directly check the random-Gaussian paradigm of the origin of the large-scale structure in the universe.