  We show that the anyonic statistics of fractionalized excitations display
characteristic signatures in threshold spectroscopic measurements. Drawing
motivation from topologically ordered phases such as gapped quantum spin
liquids and fractional chern insulators which possess fractionalized
excitations, we consider gapped systems with abelian anyonic excitations. The
low energy onset of associated correlation functions near the threshold show
universal behaviour depending on the statistics of the anyons. This explains
some recent theoretical results in spin systems and also provides a route
towards detecting statistics in experiments such as neutron scattering and
tunneling spectroscopy.
