The study of the formation and evolution of structure in the Universe, as measured through increasingly larger and deeper cosmological surveys, can help answer some of the most fundamental problems in physics - the nature of Dark Energy and Dark Matter, and the total mass of the Standard Model neutrinos. Our current understanding is based primarily on information from large scale clustering of these structures, where perturbation theory is a robust modeling tool. However, there is potentially much untapped information from the study of clustering on smaller scales. Progress in computing power and numerical simulation techniques have meant that N-body simulations can be used to accurately model structure formation into the nonlinear regime over large parts of the parameter space of interest. At the same time, there is active research into the statistical measures that can best extract information from the clustering on small scales. In this context, I will describe a novel set of summary statistics - the k-Nearest Neighbor distributions. These statistics are computationally cheap to evaluate on data, while being sensitive to all higher N-point functions, and therefore much more sensitive than the traditionally used 2-point functions. I will describe how these statistics can be used as a measure of both auto and cross-correlations in the cosmological context. I will then discuss how these statistics can be modeled for a set of tracers like galaxies in order to extract constraints on various cosmological parameters, and demonstrate the expected improvements over the 2-point function approach.
