  A random interaction matrix model is used to study the statistics of
conductance peak heights in Coulomb blockade quantum dots. When the
single-particle dynamics conserves time-reversal symmetry, the peak height
statistics is insensitive to the interaction strength. But when the
single-particle dynamics breaks time-reversal symmetry, the peak height
statistics exhibits a crossover from unitary to orthogonal symmetry as the
interaction strength increases. This crossover is driven by the time-reversal
symmetry of the interaction. Our random interaction matrix model describes
features of both the measured peak height and peak spacing statistics.
