Does anyone have a good reference or references that go into detail on rigorous/formal developments of 2-point correlation functions for curvature perturbations (and related perturbations) in the cosmological context? I'm using the TASI lectures in inflation, Mukhanov, and Dodelson but none of them go into any detail on the formal statistics of "fluctuations", what exactly in cosmological perturbation theory is randomized across a statistical ensemble and why, how the 2-point correlation is formally defined in terms of random variables, what the random variables are in inflationary cosmology, how the 2-point correlation function relates to "fluctuations" (which I take to mean the variance of a random variable), if "fluctuations" refers to fluctuations across different points in space (or equivalently, different energy scales in Fourier space) as opposed to fluctuations in a random variable at a given fixed point in space, and so on. So does anyone know of any good resources for these questions, ideally in a cosmological context (but if not I'm also happy with one in a general context or perhaps in the context of statistical mechanics since I have Kardar and Kardar's chapter on probability theory is pretty terrible)? Is Weinberg any good for this? Thanks in advance.