  We study tunneling through an edge state formed around an antidot in the
fractional quantum Hall regime using Wen's chiral Luttinger liquid theory
extended to include mesoscopic effects. We identify a new regime where the
Aharonov-Bohm oscillation amplitude exhibits a distinctive crossover from
Luttinger liquid power-law behavior to Fermi-liquid-like behavior as the
temperature is increased. Near the crossover temperature the amplitude has a
pronounced maximum. This non-monotonic behavior and novel high-temperature
nonlinear phenomena that we also predict provide new ways to distinguish
experimentally between Luttinger and Fermi liquids.
