"Local exclusion and energy bounds for intermediate and fractional statistics"
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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. I will consider applications
of recent bounds for the energy of a many-particle wave function in terms
of its density, so called Lieb-Thirring inequalities, to models of anyons
in two dimensions, as well as to models in one dimension of Lieb-Liniger
and Calogero-Sutherland type. These bounds follow from a local form of the
exclusion principle valid for such generalized exchange statistics modeled
by interactions. This is joint work with Jan Philip Solovej.