Statistics of initial density perturbations in heavy ion collisions and their fluid dynamic response

An interesting opportunity to determine thermodynamic and transport properties in more detail is to identify generic statistical properties of initial density perturbations. Here we study event-by-event fluctuations in terms of correlation functions for two models that can be solved analytically. The first assumes Gaussian fluctuations around a distribution that is fixed by the collision geometry but leads to non-Gaussian features after averaging over the reaction plane orientation at non-zero impact parameter. In this context, we derive a three-parameter extension of the commonly used Bessel-Gaussian event-by-event distribution of harmonic flow coefficients. Secondly, we study a model of N independent point sources for which connected n-point correlation functions of initial perturbations scale like 1/N^(n-1). This scaling is violated for non-central collisions in a way that can be characterized by its impact parameter dependence. We discuss to what extent these are generic properties that can be expected to hold for any model of initial conditions, and how this can improve the fluid dynamical analysis of heavy ion collisions.