Diagrammatic Methods in Statistics and Biasing in the Large-scale Structure of the Universe

Abstract

We develop technique concerning statistical analyses of the large-scale structure of the universe in the presence of biasing in the structure formation. We formulate the diagrammatic method to calculate the correlation functions of the nonlocally biased field from a generally non-Gaussian density field. Our method is based on generalized Wiener-Hermite expansion of the density field. The present formalism has not only general applicability, but also practical significance, too. To show the effectiveness of this method, we revisit the problems on biasing that have been considered previously, i.e., various approximations for peak statistics and hierarchical structure of correlation functions of locally biased field. Further analyses which have not been possible so far on these problems can be performed by our formalism. The gravitational evolution of primordial fluctuation or other structure-forming processes can be described by nonlocal biasing, so can be treated by our new formalism in principle.