  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 in a finite range of values. Some suggestions for future
single-molecule experiments are made.
