  We verify the validity of the Cohen-Gallavotti fluctuation theorem for the
strongly correlated problem of charge transfer through an impurity in a chiral
Luttinger liquid, which is realizable experimentally as a quantum point contact
in a fractional quantum Hall edge state device. This is accomplished via the
development of an analytical method to calculate the full counting statistics
(FCS) of the problem in all the parameter regimes involving the temperature,
the Hall voltage, and the gate voltage.
