  In one and two spatial dimensions there is a logical possibility for
identical quantum particles different from bosons and fermions, obeying
intermediate or fractional (anyon) statistics. We consider applications of a
recent Lieb-Thirring inequality for anyons in two dimensions, and derive new
Lieb-Thirring inequalities for intermediate statistics in one dimension with
implications for models of Lieb-Liniger and Calogero-Sutherland type. These
inequalities follow from a local form of the exclusion principle valid for such
generalized exchange statistics.
