GENUS STATISTICS OF THE LARGE-SCALE STRUCTURE WITH NON-GAUSSIAN DENSITY FIELDS

As a statistical measure to quantify the topological structure of the large-scale structure in the universe, the genus number is calculated for a number of non-Gaussian distributions in which the density field is characterized by a nontrivial function of some Gaussian-distributed random numbers. As a specific example, the formulae for the lognormal and chi(2) distributions are derived and compared with the results of N-body simulations together with the previously known formulae for th e Gaussian distribution and second-order perturbation theory. It is sh own that the lognormal formula fits most of the simulation data the be st.