  We study the transport properties of an Aharonov-Bohm ring containing two
quantum dots. One of the dots has well-separated resonant levels, while the
other is chaotic and is treated by random matrix theory. We find that the
conductance through the ring is significantly affected by mesoscopic
fluctuations. The Breit-Wigner resonant peak is changed to an antiresonance by
increasing the ratio of the level broadening to the mean level spacing of the
random dot. The asymmetric Fano form turns into a symmetric one and the
resonant peak can be controlled by magnetic flux. The conductance distribution
function clearly shows the influence of strong fluctuations.
