High-precision Monte-Carlo modelling of galaxy distribution

We revisit the case of fast Monte-Carlo simulations of galaxy positions for a non-gaussian field. More precisely we address the question of generating a 3D field with a given one-point function (as a log-normal one, but not only) and some power-spectrum fixed by cosmology. We highlight and investigate a problem that occurs when the field is filtered and identify, for the log-normal case, a regime where it can still be used. However we show that the filtering is unnecessary if one takes into account aliasing effects and finely controls the discrete sampling step. In this way we demonstrate a sub-percent precision of all our spectra up to the Nyquist frequency. We extend the method to generate a full light cone evolution comparing two methods for doing it and validate our method with a tomographic analysis. We investigate analytically and numerically the structure of the covariance matrices obtained with such simulations which may be useful for future large and deep surveys.