Non-linear theory of high order correlations
William C. Saslaw · Cambridge University Press eBooks · 1985
Like bubbles on the sea of Matter born, They rise, they break, and to that sea return Alexander Pope Equation of state Imagine life as it may have been a million years ago. You are in the jungle, being stalked by a tiger. Your ability to survive depends on pattern recognition. If you can only see the stripes on the tiger (small scale correlations), but not the overall effect of the tiger itself, you will be at some disadvantage. Perhaps this is how the ability of our eyes to recognize high order correlation functions developed. Similarly, restricting our understanding of galaxy clustering to just the two- or three-particle correlation functions means we miss a lot of the action. We need a simple measure of high order clustering which can also be related to basic gravitational physics. In Section 27 we saw that gravitational clustering can be characterized by the distribution of voids. These, in turn, are related to the high order correlations which describe the galaxies which should have been in the region of the void but are not. We may generalize the idea of a void by working in terms of distribution functions f(N) which give the probability of finding any number of galaxies in a volume V of arbitrary size and shape. For N = 0, the distribution of voids is f (0), which is calculated in (27.7) for a Poisson distribution.