All inputs of size $n$ are equally likely to occur.
It seems likely that the arguments would be much more involved.
It is highly likely that if one of the $X$'s is exchanged for another, the inequality fails.
A complete explication of the Fox spaces is warranted, as it will likely reveal further clues to the differences between the parabolic and hyperbolic theories.
This change is unlikely to affect the solution.
It is unlikely that the disturbances will eventually disappear.