From finance to cosmology: The copula of large-scale structure

Abstract

Any multivariate distribution can be uniquely decomposed into marginal (one-point) distributions, and a function called the copula, which contains all of the information on correlations between the distributions. The copula provides an important new methodology for analyzing the density field in large-scale structure. We derive the empirical two-point copula for the evolved dark matter density field. We find that this empirical copula is well approximated by a Gaussian copula. We consider the possibility that the full n-point copula is also Gaussian and describe some of the consequences of this hypothesis. Future directions for investigation are discussed. © 2010. The American Astronomical Society. All rights reserved..