  A local exclusion principle is observed for identical particles obeying
intermediate/fractional exchange statistics in one and two dimensions, leading
to bounds for the kinetic energy in terms of the density. This has implications
for models of Lieb-Liniger and Calogero-Sutherland type, and implies a
non-trivial lower bound for the energy of the anyon gas whenever the statistics
parameter is an odd numerator fraction. We discuss whether this is actually a
necessary requirement.
