Exclusion Statistics: Low-Temperature Properties, Fluctuations, Duality, and Applications

We derive some physical properties of ideal assemblies of identical particles obeying generalized exclusion statistics. We discuss fluctuations and in this connection point out a fundamental contrast to conventional quantum statistics. We demonstrate a duality relating the distribution of particles at statistics $g$ to the distribution of holes at statistics $\frac{1}{g}$. We suggest an application to Mott insulators.