  One-dimensional fractional statistics is studied using the
Calogero-Sutherland model (CSM) which describes a system of non-relativistic
quantum particles interacting with inverse-square two-body potential on a ring.
The inverse-square exchange can be regarded as a pure statistical interaction
and this system can be mapped to an ideal gas obeying the fractional exclusion
and exchange statistics. The details of the exact calculations of the dynamical
correlation functions for this ideal system is presented in this paper. An
effective low-energy one-dimensional ``anyon'' model is constructed; and its
correlation functions are found to be in agreement with those in the CSM; and
this agreement provides an evidence for the equivalence of the first- and the
second-quantized construction of the 1D anyon model at least in the long
wave-length limit. Furthermore, the finite-size scaling applicable to the
conformally invariant systems is used to obtain the complete set of correlation
exponents for the CSM.
