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 (e.g. log-normal) and some power spectrum fixed by cosmology. We highlight and investigate a problem that occurs in the log-normal case when the field is filtered, and we identify a regime where this approximation still holds. However, we show that the filtering is unnecessary if aliasing effects are taken into account and the discrete sampling step is carefully controlled. 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 this process, and validate our method with a tomographic analysis. We analytically and numerically investigate the structure of the covariance matrices obtained with such simulations which may be useful for future large and deep surveys.Key words: large-scale structure of Universe / methods: statistical