2 7 N ov 1 99 8 Hausdorff dimension , anyonic distribution functions , and duality

We obtain the distribution functions for anyonic excitations classified into equivalence classes labeled by Hausdorff dimension h and as an example of such anyonic systems, we consider the collective excitations of the Fractional Quantum Hall Effect ( FQHE ). We also introduce the concept of duality between such classes, defined by h̃ = 3 − h. In this way, we confirm that the filling factors for which the FQHE were observed just appears into these classes and the internal duality for a given class h or h̃ is between quasihole and quasiparticle excitations for these FQHE systems. Exchanges of dual pairs (ν, ν̃), suggests conformal invariance. PACS numbers: 71.10.PM, 05.30.-d, 73.40.HM