We introduce then a correlation function κd=fd/σ2. Note that κ0=1. We rewrite the variance σ2m as
σ2m=σ2m[1+2n−1∑d=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.