We describe recent measurements of the statistics and parametric corre
lations of Coulomb blockade peak heights in shape-deformable GaAs/AlxG
a1-xAs quantum dots. We find good agreement between the measured distr
ibutions of peak heights and probability distributions predicted by ra
ndom matrix theory for both B = 0 and B not equal 0. The measured magn
etic flux correlation length phi(c) is of the order of but less than o
ne flux quantum through the dot, phi(c) similar to 0.8 phi(0), inconsi
stent with phi(c) predicted by universal scaling theory for isolated c
haotic quantum dots. (C) 1997 Academic Press Limited