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Introducing the correlation function

We introduce then a correlation function κd=fd/σ2. Note that κ0=1. We rewrite the variance σ2m as

σ2m=σ2m[1+2n1d=1κd].

The code here shows the evolution of κd as a function of d for a series of random numbers. We see that the function κd approaches 0 as d.

In this case, our data are given by random numbers generated for the uniform distribution with x[0,1]. Even with two random numbers being far away, we note that the correlation function is not zero.