On four-point correlation functions in simple polymer models

We derive an exact formula for the covariance of Cartesian distances in two simple polymer models: the freely jointed chain and a discrete flexible model with nearest-neighbor interaction. We show that even in the interaction-free case, correlations exist as long as the two distances at least partially share the same segments. For the interacting case, we demonstrate that the naive expectation of increasing correlations with increasing interaction strength only holds for a finite range of values. Some suggestions for future single-molecule experiments are made.