  We consider the dephasing rate of an electron level in a quantum dot, placed
next to a fluctuating edge current in the fractional quantum Hall effect. Using
perturbation theory, we show that this rate has an anomalous dependence on the
bias voltage applied to the neighboring quantum point contact, which originates
from the Luttinger liquid physics which describes the Hall fluid. General
expressions are obtained using a screened Coulomb interaction. The dephasing
rate is strictly proportional to the zero frequency backscattering current
noise, which allows to describe exactly the weak to strong backscattering
crossover using the Bethe-Ansatz solution.
