I'm mainly trying to understand what it means for Monte Carlo samples to be correlated. Can somebody fit this into the theory of what I know about random variables, covariance and correlation?
And then specifically, when it comes to Monte Carlo path tracing (within the path integral formulation), what would the paths be analogous to? Let's say I have two variables producing paths of length $l$. The way I understand it right now is that they produce samples from a $3l$-dimensional space -- 3 cartesian coordinates, one for each point on the path. Is this correct?
If I had two random variables generating paths of some length $l$, how would I measure the correlation?